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8112019 Toolbox 4

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APPLIED INDUSTRIAL ENERGY AND ENVIRONMENTAL MANAGEMENT

Z K Morvay D D Gvozdenac

Part III

FUNDAMENTALS FOR ANALYSIS AND CALCULATION OF ENERGY AND

ENVIRONMENTAL PERFORMANCE

1

Applied Industrial Energy and Environmental Management Zoran K Morvay andDusan D Gvozdenac copy John Wiley amp Sons Ltd

Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHERENGINEERING DATA

SI UNITS

1 The System I nternational (SI) This came into being in October 1960 and has ever since been recognized officially and adopted bynearly every country although its actual use varies considerably It is based on seven principal unitsone in each of seven different categories

Table 41 The SI Seven Principal UnitsCategory Name Abbr eviation

Length Meter mMass Kilogram kgTime Second sElectric current Ampere ATemperature Kelvin KAmount of substance Mole molLuminous intensity Candela cd

From these basic units many other unitsare derived and named

2 Definiti ons of th e Seven B asic SI Units meter [m]

Meter is a basic unit of length It is the distance light travels in a vacuum in 1299 792 458th of a second

kilogram [kg] Kilogram is a basic unit of mass It is the mass of an international prototype in the form of a platinum-iridium cylinder kept at Sevres in France It is now the only basic unit still defined interms of a material object and also the only one with a prefix [kilo] already in place

second [s] Second is a basic unit of time It is the length of time taken for 9 192 631 770 periods of

vibration of the cesium-133 atomampere [A]

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Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA2

Ampere is a basic unit of electric current It is that current which produces a specified force between two parallel wires which are 1 meter apart in a vacuum

kelvin [K] Kelvin is a basic unit of temperature It is 127316th of the thermodynamic temperature ofthe triple point of water

mole [mol] Mole is a basic unit of substance It is the amount of substance that contains as manyelementary units as there are atoms in 0012 kg of carbon-12

candela [cd] Candela is a basic unit of luminous intensity It is the intensity of a source of light of aspecified frequency which gives a specified amount of power in a given direction

3 Deri ved Uni ts of the SIFrom the seven basic units of the SI other units are derived for a variety of purposes Only a few ofthem are explained here as examples

farad [F]Farad is the SI unit of the capacitance of an electrical system that is its capacity to storeelectricity

hertz [Hz]Hertz is a SI unit for the frequency of a periodic phenomenon One hertz indicates that onecycle of the phenomenon occurs everysecond

joule [J]Joule is a SI unit of work or energy One joule is the amount of work done when an appliedforce of 1newton moves through a distance of 1meter in the direction of the force

newton [N] Newton is a SI unit of force One newton is the force required to give a mass of 1kilogram an acceleration of 1meter per second ohm [Ω] Ohm is a SI unit of resistance of an electrical conductor

pascal [Pa] Pascal is a SI unit of pressure One pascal is the pressure generated by a force of 1newton acting on an area of 1square meter volt [V] Volt is a SI unit of electric potential One volt is the difference of potential between two points of an electrical conductor when a current of 1ampere flowing between those pointsdissipates a power of 1watt

watt [W]

Watt is used to measure power or the rate of doing work One watt is a power of 1 joule persecond

4 The SI allows the sizes of units to be made bigger or smaller by the use of appropriate prefixes

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Table 42 Prefixes of Unitsyotta [Y] = 10+ zetta [Z] = 10+21 exa [E] = 10+18

peta [P] = 10+15 tera [T] = 10+12 giga [G] = 10+9

mega [M] = 10+6 kilo [k] = 10+3 hecto [h] = 100deca [da] = 10

deci [d] = 01centi [c] = 001milli [m] = 10-3 micro [micro] = 10-6 nano [n] = 10-9

pico [p] =10-12 femto [f] = 10-15 atto [a] = 10-18

zepto [z] = 10-21 yocto [y] = 10-24

1

5 SI uni tes and conversion factors For other systems of measurement these are as follows

Table 43 Conversion Factors

Name SI uni tConversion factor s for most fr equently used uni ts of other

systems and non-system uni tsAcceleration linear ms 1 ins = 00254 ms

Area m2 1 ft = 00929 m1 in = 6451times10- m

Density kgm3

1 tonm = 1 kgdm = 1 gcm = 10 kgm1 (kgf s2)m4 = 981 kgm3 1 lbft = 1602 kgm1 lbin3 = 2768times103 kgm3

Density of heat flux Wm 1 kcalm = 1163 WmDiffusion coefficient m s 1 ft s = 00929 m s

Energy work quantity of heat J

1 kWh = 36times10 J1 kcal = 41868 kJ = 41868times10 J1 lbf timesft = 1356 J1 lbf timesin = 0133 J1 BTU = 10551 J

Enthalpy specific Jkg 1 kcalkg = 1 calg = 4190 Jkg1 BTUlb = 2326 Jkg

Entropy specific J(kg K) 1 kcal(kg K) = 4190 J(kg K)1 BTU(lboF) = 4190 J(kg K)

Force (weight) N

1 kgf = 981 N1 dyn = 10- N1 sn = 103 N1 lbf = 445 N

Frequency Hz1 s-1 = 1 Hz1 rps = 1 Hz1 rpm = 160 Hz

Heat capacity specific J(kg K) 1 kcal(kg K) = 4190 J(kg K)1 BTU(lboF) = 4190 J(kg K)

Heat transfer coefficient individualand overall W(m2 K) 1 kcal(kg K) 4190 J(kg K)

1 BTU(ft hoF) = 56 W(m K)

Length m

1 microm (micron) = 10-6 m1 Aring =10- m1 ft (lsquo) = 03048 m1 in (lsquo) = 00254 m

Mass kg 1 ton (m3tric) = 1000 kg1 lb = 0454 kg

Power W

1 (kgf m)s = 981 W

1 kcalh = 1163 W1 (lbf ft)s = 1356 W1 hp = 7353 W

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Pressure Pa

1 bar = 10 Pa1 mbar = 100 Pa1 kgfcm = 1 at = 735 mm Hg = 981times10 Pa1 atm = 760 mm Hg = 101325 Pa1 kgfm = 981 Pa1 mm H2O = 981 Pa1 mmHg = 1333 Pa1 lbfin = (psi) = 689476 Pa1 lbfft2 = 4788 Pa

Rate of flow mass kgs 1 lbs = 0454 kgs1 lbh = 126times10- kgs

Rate of flow volumetric m3s1 lmin = 1667timesm s1 ft s = 283times10- m s1 in s = 164times10- m s

Specific heat of phase transition Jkg 1 kcalkg = 4189 Jkg1 BTUlb = 2326 Jkg

Surface tension Nm 1 kgfm = 981 Jm = 981 Nm

Thermal conductivity W(m K) 1 kcal(m h K) = 1163 W(m K)

1 BTU(ft ho

F) = 173 W(m K)Time s 1 h = 3600 s

1 min = 60 s

Temperature Kt [oC] = (t + 27315) [K]

t [oF] = 15273)32t(95 [K]

Velocity angular radssrad

30rpm1

srad2rps1 Velocity linear ms 1 fts = 03048 ms

Viscosity dynamic Pa s 1 P (poises)= 01 Pa s1 cP (centipoises) = 19180 kgf sm2 = 10-3 Pa s

Viscosity kinematic m2s1 S (stokes) = 1 cm s = 10- m s1 ft2s = 0093 m2s1 ft h = 2581 m s

Volume m3 1 l = 10-3 m3 1 ft = 283 dm = 00283 m1 in = 16387 cm = 1639times10- m

Volume specific m3kg 1 m3ton = 10-3 m3kg1 lkg = 1 cm g = 10-3 m kg

Note The values of the conversion factors are given with the sufficient accuracy for engineering calculations

A USEFUL DEFINITION FOR ENERGY ANALYSIS

6 The ton of oil equivalent (toe) is a unit for measuring energy It corresponds to10 Gcal or41868 GJ or 1163 MWh It is a rounded amount of energy that would be produced by burning onemetric ton of crude oil Since crude oil of different origin has different chemical properties andtherefore gives off varying amounts of heat when burnt the value is a matter of consensus to a certainextent toe is A particularly useful unit for quantifying energy production or consumption for onecountry or for the entire world

7 The most useful and practical definition ofenergy is that it is a measur e of the capacity f ordoing work Energy comes from many sources ndash sunlight wind water coal oil gas etc and it hasmany types thermal electrical chemical nuclear etc

Specif ic energy is a measure of the amount of energy contained in a single quantity of somesubstance It is also known ascalorific value

The energy content can be expressed in any unit of energy BTU calories joules watt-hours etcThe preferred unit is joules with the appropriate range of prefixes for kilojoules [kJ] megajoules[MJ] etc

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The unit quantity may be either of mass (kg) or of volume (cubic meters) It depends on the natureof the substance For solids it is usual to use unit mass and for gases to use unit volume (togetherwith a statement of pressure and temperature) For liquids either mass or volume can be used

The approximate Specific Energy values (NCV1 LCV2) of some solid fuels areCoal 23 to 35 MJkgWood 16 to 21 MJkgPeat 23 MJkgCharcoal 28 to 33 MJkg Natural uranium ndash in light water reactor 443 000 MJkgEnriched uranium (35 ) ndash in light water reactor 3 456 000 MJkgUranium - in fast breeder reactor 24 000 000 MJkg

The approximate Specific Energy values (NCV LCV) of some gas fuels areCoal gas 19 to 22 MJmsup3 Natural gas 37 MJmsup3Acetylene 56 MJmsup3Propane 93 MJmsup3Butane 110 MJmsup3

All are based on particular pressure and temperature Gas heating value varies with thegeographical location

Standard metric gas conditions are 101325 kPa and 15oC (dry)Normal metric gas conditions 101325 kPa and 0oC (dry)The approximate specific energy values (LCV) of some liquid fuels are

Gasoline 421 MJkgPetroleum 398 MJkgDiesel 418 MJkgHeavy Fuel Oil 418 MJkg

Higher Heating Value (HHV) Gross Heating Value (GHV) Gross Calorific Value (GCV) and

Total Calorific Value (TCV) are different terms for the same value This can be defined as total heatobtained from combustion of a specified amount of fuel and its stoichiometrically correct amount ofair both being at 1556oC (60 oF) when combustion starts and the combustion products being cooledto 1556oC (60 oF) before heat release is measured

Lower Heating Value (LHV) Net Heating Value (NHV) Low Calorific Value (LCV) is lowerthan Total Calorific Value for the value of latent heat of vaporization of water formed in combustion

Some typical values for the ratio of net to gross values are as followsF uel NetGr oss Ratio Natural gas 090Fuel oil 094Coal 098

Nuclear energy is totally different in both the method of production and the scale of released

energy As a very rough guide the fission of a given mass of a suitable material (such as plutonium) produces something of the order of 3 million times the energy obtained from the same mass of anlsquoordinaryrsquo fuel such as coal

8 Density is mass of fluid in a unit volume [kgm3]

9 Dynami c viscosity is the tangential force per unit area required to move one horizontal planewith respect to the other at unit velocity when maintained at a unit distance apart by the fluid Itappears as a result of cohesion and interaction between molecules

1 NCV ndash Net Calorific Value

2 LCV ndash Low Calorific Value (NCV = LCV)

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Different fluids deform at different rates under the same shear forces Fluid with a high viscositysuch as syrup deforms more slowly than fluid with a low viscosity such as water

Newtonian fluids obey the linear relationship given by the Newtons law of viscositydxdw

where is the shear stress and micro is the coefficient of dynamic viscosityViscosity is resistance of a fluid to flow This resistance acts against the motion of any solid

object through the fluid and also against motion of the fluid itself past stationary obstacles Viscosityalso acts internally on the fluid between slower and faster moving adjacent layers

All fluids (liquids and gases) exhibit viscosity to some degree Viscosity may be thought of asfluid friction just as the friction between two solids resists the motion of one over the other but alsomakes possible the acceleration of one relative to the other

The dynamic viscosities of some fluids are presented in Table 44 It is very important to know thetemperature of the fluid (and pressure)

Table 44 Dynamic Viscosity of Some Liquids and GassesLiquid Gas

Gasoline Water Air (dry)1013 bar

Carbon Dioxide1013 bar

t (oC) Μ [Pa s] t (oC) μ

[Pa s] t (oC) μ [Pa s] t (oC) μ

[Pa s]20 0529times10-3 0 1780times10-3 0 0017times10-3 0 0014times10-3 40 0411times10- 20 1004times10- 100 0022times10- 100 0018times10- 60 0328times10-3 40 0653times10-3 200 0026times10-3 200 0023times10-3 100 0225times10- 60 0470times10- 300 0030times10- 300 0026times10-

80 0355times10-3 400 0033times10-3 400 0030times10-3 100 0283times10- 500 0036times10- 500 0033times10-

10 Kinematic viscosity is the ratio of absolute viscosity to density For either dynamic orkinematic viscosity to be meaningful a reference temperature must be quoted

11 Thermal conductivi ty is a measurement of the ability of a material to conduct heat It isdefined using the Fouriers law of conduction which relates the rate of heat transfer by conduction tothe temperature gradient

dxdT

Ak q (41)

where k is the thermal conductivity Using the Fouriers law we can define the thermal conductivityas the rate of heat transfer through a unit thickness of material per unit area and per unit temperaturedifference A good conductor of heat has a high value of thermal conductivity

The temperature variations of the thermal conductivities of some materials are presented in Table5

Table 45 Thermal Conductivity of Some Materials ndash k [W(m K)]

t (oC)Solid Liquid Gas

Copper Aluminum Gasoline Water Air (dry)1013 bar

Steam(saturated)

-100 407 -0 386 221 00244 001760

100 379 - 01005 00680 00321 002372200 373 229 00670 00393 003547300 - 222 00558 00460 006270

500 - - 00574700 - - 00671

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12 Specif ic heat is the amount of heat that is required to raise the temperature of the unit mass ofa substance by one degree In a constant pressure process

Tcmq p (42)

c p is specific heat at constant pressureValues of c p [kJ(kg K)] for various materials (at 20oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp kJ(kg K) LIQUID cp

kJ(kg K) GAS cp kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047Gold 0129 Gasoline 206 Sulfur Dioxide 0633Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coeff icient of thermal expansion is defined as the change in the density of a substance as afunction of temperature at constant pressure It is expressed as follows

pT1 (43)

For ideal gases TR p there is

T1

14 Thermal diff usivity is measure of heat propagation through a medium and may be defined bythe ratio of heat conducted through a material to the heat stored in the material The thermaldiffusivity is defined as

pck

a (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If thethermal diffusivity is small it means that a large part of heat is absorbed by the material and only asmall portion is conducted through it Some typical values of thermal diffusivity are given in Table47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID am 2s LIQUID a

m 2s GAS am 2s

Aluminum 93166times10- Water 0131times10- Air 18777times10- Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6 Gold 12479times10- Gasoline 0075times10- Sulfur Dioxide 4711times10- Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

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PHYSICAL PROPERTIES

15 Physical Properti es of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

MaterialDensity Molar

MassGas

ConstBoilingPoint cp cpcv 10 6 timesmicro K Pr

kgm 3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -Air (dry) 1293 2895 287 -195 1010 14 173 00245 071Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064Carbon Dioxide[CO2]

1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074 Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077 Normal composition of clean dry atmospheric air near the sea level Nitrogen (N 2 ) =78084 Oxygen (O 2 ) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO 2 ) =0031 Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H 2 ) Xenon (Xe) Methane (CH 4 ) Nitrogen Oxide (N 2O) Ozone (O 3 )Sulfur Dioxide (NO 2 ) Ammonia (NH 3 ) Carbon Monoxide (CO) and Iodine (I 2 ) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash c p [kJkg] of various gases inthe range from 0 to 2000oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maximum

Error

Hydrogen (H2) 01+143810E+t04-200328E+t08-356131E-t10-342031E+t13-108329E-= 234 006 Nitrogen (clean)

(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009

Oxygen (O2) 01-907389Et04-144682Et08-150961Et11-443486E-t14-123574E= 234 012Carbon Monoxide

(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006

Water Vapor (H2O) 00185773Et04-135306Et07-267351Et10-142139E-t14-235461E=234

004Sulfur Dioxide(SO2) 01-606803Et04-321094Et07-201319E-t11-653115Et15-804281E-= 234 012

Air 00100361Et05-218551Et07-142841Et11-968901E-t14-199627E= 234 009 Nitrogen (form Air)

(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

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16 Physical Pr operties of Selected Liqu ids

Table 410 Physical Properties of Selected Liquids

Liquid t [ oC] ρ [kgm 3]cp [kJkg

K)]

k [W(m

K)]

micro times 10 3 [Pa

s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302

17 Thermodynamic and Tr ansport Pr oper ties of Water and Steam

a

Some of thermodynamic properties of water areH2O = Chemical formulaM = 18016 [kgkmol] (Molecular Mass)tc = 37415 [oC] (Critical Temperature)Tc = 647286 [K] (Absolute Critical Temperature) pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)tm = 001 [oC] (Melting Temperature at 101325 bar)r m = 332432 [kJkg] (Heat of Melting at 101325 bar)t b = 1000 [oC] (Boiling Temperature at 101325 bar)r b = 22570 [kJkg] (Heat of Evaporation at 101325 bar)R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature andpressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

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a Satur ated steam and boil ing water temperatur e versus pressur e 3

112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)

Error is in the range 007

b Satur ated steam and boil ing water pressur e versus temperatur e

5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boili ng water versus temperature

1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)

d En thal py of satur ated steam versus temperatur e

250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)

e En tr opy of boil in g water versus pressur e

130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)

f En tr opy of saturated steam versus pressure

736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)

Water properties (temperatures from 0 to 300oC)(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)

3 ln - natural logarithm

8112019 Toolbox 4




h Specif ic heat at constant pressur e c p [J(kg K)]

30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)

j Thermal diff usivity a [m 2 s]

pc

a (414)

k Dynamic viscosity [Pa s]

748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)

l Ki nematic viscosi ty [m 2 s]

(416)

m Coeffi cient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obviousthat they depend on temperature much more than on pressure Because of that for almost all industrialcalculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versusTemperature and Pressure

]mkg[ 3 )]K kg(J[c p )]K m(W[ ]sPa[10 6

] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297+ p0554983+ p000557908- p8000014411= 23 (418)

o Specif ic heat at constant pressur e of satur ated steam

186459+t0784614+t000461955+t93000009956=c 23 p (419)

p Thermal conductivi ty of satur ated steam

0404835-t00474611+t8000026173-t3939000000064=10 232 (420)

q Dynamic viscosity of satur ated steam

81587+t00375325+t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]K kg(J[c p )]K m(W[10 2 ]sPa[10 6 p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4




18 Physical Properties of Selected Soli d M aterials

Table 413 Properties of Selected Solids at 25 oC

Substancekgm 3

pc

[kJ(kg K)]

Asphalt 2120 167Brick (common) 1800 084Carbon (diamond) 3250 051Carbon (graphite) 2000 ndash 2500 061Coal 1200 ndash 1500 126Concrete 2200 088Glass (plate) 2500 080Glass (wool) 200 066Granite 2750 089Ice (0 oC) 917 204Paper 700 120Plexiglas 1180 144Polystyrene 920 230Polyvinyl chloride 1380 096Rubber (soft) 1100 167Salt (rock) 2100 ndash 2500 092Sand (dry) 1500 080Silicon 2330 070Snow (firm) 560 210Wood (hard oak) 720 126Wood (soft pine) 510 138Wool 100 172

Table 414 Properties of Selected Metals at 25oC

Metalskgm 3

pc

[kJ(kgK)]

Aluminum 2700 090Copper (commercial) 8300 042Brass (60-40) 8400 038Gold 19300 013Iron (cast) 7272 042Iron (Steel 304 St) 7820 046Lead 11340 013Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044Silver (999 Ag) 10524 024Sodium 971 121Tin 7304 022Tungsten 19300 013Zinc 7144 039

8112019 Toolbox 4




Table 415 Thermal Expansion Coefficients andThermal Conductivity of Solids

Material

Thermal

ExpansionCoefficient(times10 -6ordmC)

ThermalConductivity

(WmmiddotK)

Aluminum 230 237Aluminum Alloy 230 ndash Brass 191 ndash 212 ndash Brass Noval 211 ndash Brass Red (80 Cu20 Zn) 191 ndash

Brick 500 ndash 700 ndash Bronze Regular 180 ndash 210 ndash Bronze Manganese 200 ndash Concrete 700 ndash 140 ndash Copper 166 ndash 176 410

Copper Alloy 170 ndash Glass 500 ndash 110 ndash Gold ndash 317Iron ndash 802Iron (Cast) 990 ndash 120 ndash Iron (Wrought) 120 -Lead ndash 353Magnesium 252 156Magnesium Alloy 261 ndash 288 ndash Monel (67 Ni 30Cu) 140 ndash

Nickel 130 907 Nylon Polyamide 750 ndash 100 ndash Platinum ndash 716Rubber 130 ndash 200 ndash Silicon ndash 148Silver ndash 429Solder Tin-Lead ndash 300 ndash 498Steel 100 ndash 180 ndash Tin ndash 666Titanium ndash 219Titanium Alloy 800 ndash 100 ndash Tungsten 430 174Zinc 302 116

Table 416 Density Melting and Boiling Points ofSolids

Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

Point[oC]Aluminum 271 6603 2519

Aluminum Alloy 264 ndash 28

5650 ndash 6600 ndash

Brass 84 ndash 875 9300 ndash

Brass Noval 84 ndash ndash Brass Red (80 Cu 20Zn) 875 1000 ndash

Brick (Compression) 18 ndash 24 ndash - ndash

Bronze Regular 78 ndash 88 1050 ndash

Bronze Manganese 83 ndash ndash Carbon 225 4492 3642Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash 24 ndash ndash

Copper 894 1085 2562Copper Alloy 823 9250 ndash

Cork 015 ndash 02 ndash ndash

Glass 24 ndash 28 ndash ndash

Gold 1932 1064 2856Iron (Cast) 787 1538 2861Iron (Wrought) 7 ndash 74 ndash ndash -

Magnesium [Mg] 74 ndash 78 ndash ndash

Magnesium Alloy 113 3275 1749Monel (67 Ni 30 Cu) 174 6500 1090 Nickel [Ni] 177 1246 2061 Nylon Polyamide 884 1330 ndash Platinum 889 1455 2913Rubber 11 - -Silver 214 1768 3825

Solder Tin-Lead 096 ndash 13 ndash ndash

Steel 233 1382 ndash Stone Granite(Compression) 1049 9618 2162

StoneLimestone (Compression)

817 ndash 1134 2150 ndash

Stone Marble(Compression) 785 1425 ndash

Tin 26 ndash ndash Titanium 2 ndash 29 ndash ndash

Titanium Alloy 26 ndash 29 ndash ndash

Wood Ash (Bending) 26 ndash ndash Wood Douglas Fir(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287Wood Southern Pine(Bending) 451 ndash ndash

Zinc 193 3422 5555

8112019 Toolbox 4




19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why theyare accorded such special attention in this Toolbox This paragraph provides all of the relevantconstants and equations used for the creation of software which enables the computation of thethermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]2 Given T [oC] and P [bar]3 Given T [oC] and h [kJkg]4 Given T [oC] and s [kJ(kg K)]5 Given v [m3kg] and P [bar]6 Given v [m3kg] and h [kJkg]7 Given v [m3kg] and s [kJ(kg K)]8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value islower than the critical one

ConstantsTc = 647286 K R = 461518 [J(kg K)] E = 00048Pc = 22089 MPa T p = 33815 a = 001ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T

A)E1(AEe)1i(AQ (424)

and

TTa 732 jfor 52 jac1a

6341a 732 jfor 1000 ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848A(10 1) = -00004160586

8112019 Toolbox 4




A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T( p p satsatsat

8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f =

f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] ischosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgf fg dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

8112019 Toolbox 4




fgvf hhh (432)

The entropy of vaporization is given by

T

hs fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom Reynolds WC (1979) Thermodynamic Properties in SI Stanford University StanfordSonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Incwwwchemputecomftphtm wwwchemicalogiccom The Engineering Toll Box wwwengineeringtollboxcom

8112019 Toolbox 4




Ampere is a basic unit of electric current It is that current which produces a specified force between two parallel wires which are 1 meter apart in a vacuum

kelvin [K] Kelvin is a basic unit of temperature It is 127316th of the thermodynamic temperature ofthe triple point of water

mole [mol] Mole is a basic unit of substance It is the amount of substance that contains as manyelementary units as there are atoms in 0012 kg of carbon-12

candela [cd] Candela is a basic unit of luminous intensity It is the intensity of a source of light of aspecified frequency which gives a specified amount of power in a given direction

3 Deri ved Uni ts of the SIFrom the seven basic units of the SI other units are derived for a variety of purposes Only a few ofthem are explained here as examples

farad [F]Farad is the SI unit of the capacitance of an electrical system that is its capacity to storeelectricity

hertz [Hz]Hertz is a SI unit for the frequency of a periodic phenomenon One hertz indicates that onecycle of the phenomenon occurs everysecond

joule [J]Joule is a SI unit of work or energy One joule is the amount of work done when an appliedforce of 1newton moves through a distance of 1meter in the direction of the force

newton [N] Newton is a SI unit of force One newton is the force required to give a mass of 1kilogram an acceleration of 1meter per second ohm [Ω] Ohm is a SI unit of resistance of an electrical conductor

pascal [Pa] Pascal is a SI unit of pressure One pascal is the pressure generated by a force of 1newton acting on an area of 1square meter volt [V] Volt is a SI unit of electric potential One volt is the difference of potential between two points of an electrical conductor when a current of 1ampere flowing between those pointsdissipates a power of 1watt

watt [W]

Watt is used to measure power or the rate of doing work One watt is a power of 1 joule persecond

4 The SI allows the sizes of units to be made bigger or smaller by the use of appropriate prefixes

8112019 Toolbox 4









zepto [z] = 10-21 yocto [y] = 10-24

1






Density kgm3







Force (weight) N






Length m



Power W

1 (kgf m)s = 981 W


8112019 Toolbox 4




Pressure Pa







1 BTU(ft ho

F) = 173 W(m K)Time s 1 h = 3600 s

1 min = 60 s


t [oF] = 15273)32t(95 [K]


30rpm1












8112019 Toolbox 4




















8112019 Toolbox 4



















dxdT

Ak q (41)






Steam(saturated)

-100 407 -0 386 221 00244 001760

100 379 - 01005 00680 00321 002372200 373 229 00670 00393 003547300 - 222 00558 00460 006270

500 - - 00574700 - - 00671

8112019 Toolbox 4





Tcmq p (42)







pT1 (43)


T1


pck

a (44)




m 2s GAS am 2s


8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4









zepto [z] = 10-21 yocto [y] = 10-24

1






Density kgm3







Force (weight) N






Length m



Power W

1 (kgf m)s = 981 W


8112019 Toolbox 4




Pressure Pa







1 BTU(ft ho

F) = 173 W(m K)Time s 1 h = 3600 s

1 min = 60 s


t [oF] = 15273)32t(95 [K]


30rpm1












8112019 Toolbox 4




















8112019 Toolbox 4



















dxdT

Ak q (41)






Steam(saturated)

-100 407 -0 386 221 00244 001760

100 379 - 01005 00680 00321 002372200 373 229 00670 00393 003547300 - 222 00558 00460 006270

500 - - 00574700 - - 00671

8112019 Toolbox 4





Tcmq p (42)







pT1 (43)


T1


pck

a (44)




m 2s GAS am 2s


8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4




Pressure Pa







1 BTU(ft ho

F) = 173 W(m K)Time s 1 h = 3600 s

1 min = 60 s


t [oF] = 15273)32t(95 [K]


30rpm1












8112019 Toolbox 4




















8112019 Toolbox 4



















dxdT

Ak q (41)






Steam(saturated)

-100 407 -0 386 221 00244 001760

100 379 - 01005 00680 00321 002372200 373 229 00670 00393 003547300 - 222 00558 00460 006270

500 - - 00574700 - - 00671

8112019 Toolbox 4





Tcmq p (42)







pT1 (43)


T1


pck

a (44)




m 2s GAS am 2s


8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4




















8112019 Toolbox 4



















dxdT

Ak q (41)






Steam(saturated)

-100 407 -0 386 221 00244 001760

100 379 - 01005 00680 00321 002372200 373 229 00670 00393 003547300 - 222 00558 00460 006270

500 - - 00574700 - - 00671

8112019 Toolbox 4





Tcmq p (42)







pT1 (43)


T1


pck

a (44)




m 2s GAS am 2s


8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4



















dxdT

Ak q (41)






Steam(saturated)

-100 407 -0 386 221 00244 001760

100 379 - 01005 00680 00321 002372200 373 229 00670 00393 003547300 - 222 00558 00460 006270

500 - - 00574700 - - 00671

8112019 Toolbox 4





Tcmq p (42)







pT1 (43)


T1


pck

a (44)




m 2s GAS am 2s


8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4





Tcmq p (42)







pT1 (43)


T1


pck

a (44)




m 2s GAS am 2s


8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4




PHYSICAL PROPERTIES




MassGas



1976 4401 189 - 837 13 137 00137 084





Gas


])C[t()Kkg(kJ[c ot

op


Maximum

Error


(N2)00103937Et06-857115Et07-173326Et10-106900E-t14-207571E= 234 009


(CO) 00103823Et05-124096Et07-176241Et10-120740E-t14-251706E 234 011

Carbon Dioxide(CO2)

01-820310Et04-516236Et07-298914E-t10-104359Et14-156925E-= 234 006




(N2)00102694Et05-142726Et07-131381Et11-797576E-t14-148364E= 234 014

8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4







K)]

k [W(m

K)]


s]

β times 10 5

[1K]a [m 2s]

Acetone2050

791756

216225

01700163

0331-

143-

Gasoline

204060

100

751735717681

206215224246

01165--

01005

0529041103280225

125---

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol02050

806789

-

229245281

018501830178

1781190695

EthyleneGlycol

204060

80100

111310991085

10701056

238224742562

26502742

0258--

-0269

1990913495

302199

Glycerin

2050

100200

1260124412001090

235250279334

-02830289

-

148018013

022

53---

Methyl Alcohol02050

810792765

243247256

02410212

-

081805850400

Petroleum

2050

100200

819801766785

200214238289

-011140104200891

149095605450262

100---

Oil (lubricant)

255075

100

920905896880

1850194320412136

0130012801250123

190429156572

Oil(transformer)

255075

100

860845835820

1918204321692294

0123012201200117

2420990477302


a




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4





112

31-42-

5-36-5

109963430ln(p)][102794824ln(p)][2397684

ln(p)][102118802ln(p)][101786280

ln(p)][101285144ln(p)][1005-5518190Et

(45)



5098158]-t107261845t102974345-t101096061

t103381446-t107363934t10316exp[-7789 p2-24-36-

4-95-126-15

(46)



1-

2-53-74-9

10359463t417927

t10723854-t10706612t10833022h (47)


250044t187334

t10103177-t10151237t10332313-h 2-33-64-8

(48)


130250ln(p)10315672

(ln(p))10167802(ln(p))10145398(ln(p))10973390s2-

2-33-44-5

(49)


736130ln(p)10336497-(ln(p)10760363(ln(p)10-538843s -12-43-4 (410)


g Density [kgm 3 ]

22-23-

3-54-75-106-13

10999945t10410381t10726539-

t10428877t10208168-t10556465t10-644703 (411

)


8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4





30-21-

3-34-65-86-11 p

10421629t10370637-t10109452

t10142353-t10976851t10317259-t10400424c (412

)


11-23-

3-64-95-116-112

10549688t10285413t10210253-

t10672554t10740918-t10187737-t1036594410 (413

)


pc

a (414)


748230t10322128-t10218237

t10103401-t10272328t1077Exp(-2918102-22-

3-64-95-126

(415)


(416)


1-1-23-35-

4-85-106-134

10684475-t10163711t10182013-t10158931

t10746034-t10170218t10-12877310 (417

)




] bar [ p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o 0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 129520 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 100130 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 80340 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 65750 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 55460 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 47570 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4




80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 36090 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287150 9221 9273 4275 4237 0693 0699 188 190200 8707 8776 4455 4396 0672 0679 138 140250 8059 8161 4781 4681 0624 0636 112 115300 7154 7346 5661 5275 0542 0558 91 94350 6006 8206 0452 75360 547 12560 0412 69



00203297+ p0554983+ p000557908- p8000014411= 23 (418)


186459+t0784614+t000461955+t93000009956=c 23 p (419)


0404835-t00474611+t8000026173-t3939000000064=10 232 (420)


81587+t00375325+t281000000762=10 26 (421)




t [ oC]

220 9588 2935 373 168230 9285 2784 383 174240 9025 2633 393 177250 8787 1962 2554 3647 403 453 181 183280 2937 4438 532 198290 2808 4028 505 202300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289550 1606 2353 784 312

8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4






Substancekgm 3

pc

[kJ(kg K)]



Metalskgm 3

pc

[kJ(kgK)]



8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4





Material

Thermal


ThermalConductivity

(WmmiddotK)






Material

Density

[times1000kgm 3]

Melting

Point[oC]

Boiling

























Zinc 193 3422 5555

8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4











a = 001


T

2 QQ1TR P (422)

Where

7

1 j

8

1i

10

9i

9i ji

E1i ja ji

2 j jac AeAQ (423)

7

1 j

8

2i j10 j9

E2i ja ji

2 j jac

T


and


6341a 732 jfor 1000 ja


8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4





A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253A(10 7) = 0000071531353


0v

6

1i

2i0v T)i(Gc (425)

whereG(1) = 46000G(2) = 1011249G(3) = 083893G(4) = -0000219989G(5) = 0000000246619G(6) = -0000000000097047


8

1i

)1i( psat

sat

c

c

tsa TTa)i(F1TT

P

pln (426)

where

F(1) = -7419242F(2) = 029721F(3) = -01155286F(4) = 0008685635F(5) = 0001094098

8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4




F(6) = -000439993F(7) = 0002520658F(8) = -00005218684


f (Tsat)

8

1i

3i

ccf T

T1)i(D1 (427)

whereD(1) = 36711257D(2) = -28512396D(3) = 2226524D(4) = -88243852D(5) = 20002765D(6) = -26122557

D(7) = 18297674D(8) = -5335052


dTP

TP1

dT)T(cuu0

2

T

T

0v0

0

(428)



vPuh (429)


uo = 23750207 [Jkg]


dT

PR

1)ln(R dT

T

)T(css

02

T

T

0v

0

0

(430)


so = 66965776 [J(kg K)]


sat

satgf fg dT

dPvvTh (431)


8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




8112019 Toolbox 4




fgvf hhh (432)


T

hs fg

fg (433)


fgvf sss (434)




toolbox 4

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