thermodynamics lecture series

Thermodynamics Lecture Series

email: [email protected]://www.uitm.edu.my/faculties/fs

g/drjj1.html

Applied Sciences Education Research Group (ASERG)

Faculty of Applied SciencesUniversiti Teknologi MARA

Gas Mixtures – Gas Mixtures – Properties and Properties and

BehaviourBehaviour

Review – Steam Power Plant

Pum

p

Boiler Turbine

Condenser

High T Res., TH

Furnace

qin = qH

in

out

Low T Res., TL

Water from river

A Schematic diagram for a Steam Power Plant

qout = qL

Working fluid:Water

qin - qout = out - in

qin - qout = net,out

Review - Steam Power Plant

Steam Power Plant

High T Res., TH

Furnaceqin = qH

net,out

Low T Res., TL

Water from river

An Energy-Flow diagram for a SPP

qout = qL

Working fluid:Water

Purpose:Produce work,

Wout, out

Review - Steam Power Plant

Thermal Efficiency for steam power plants

in

out,net

qnputi equiredroutput desired

in

out,net

q

in

outin

qqq

in

out

qq1

H

L

qq1

H

Lrev T

T1 For real engines, need to find qL and qH.

Entropy Balance –Steady-flow deviceReview - Entropy Balance

Heat exchanger

Qin1

2

4

3, Hot water inlet

Cold water Inlet Out

Case 1 – blue border

Case 2 – red border


outinoutin WWQQ

kW ,)()( inletexit mm

Heat exchanger: energy balance;

kW,hmhmhmhm0 11223344

Assume kemass = 0, pemass = 0

where 34 mm

1 2

4

3Qin

Case 1

kW ,hhmhhm 212344

12 mm


Heat exchanger: energy balance;

Assume kemass = 0, pemass = 0

where

kW ,mmQQ 1122outin

1 2

4

3Qin

kW ,hhm0Q 122in

Case 1Case 2

kW ,hhmhhm 212344

34 mm

12 mm


Heat exchanger:

KkW,smsmsmsm00S 11223344gen

Entropy Balancewhere

1 2

4

3Qin

Case 134 mm

12 mm

K

kW ,ssmssmS 122344gen


KkW,smsm

TQ

TQS 1122

in

in

out

outgen

Heat exchanger:Entropy Balance

where1 2

4

3Qin

Case 234 mm

12 mm

K

kW ,ssmTQ0S 122

in

ingen

T- s diagram for an Ideal Rankine CycleVapor Cycle – Ideal Rankine Cycle

T, C

s, kJ/kgK

1

2

Tcrit

TH

TL= Tsat@P4

Tsat@P2

s3 = s4s1 = s2

qin = qH

4

3

PH

PL

in

out

pump

qout = qL

condenser

turbineboiler

s1 = sf@P1 h1 = hf@P1

s3 = s@P3,T3

s4 = [sf +xsfg]@P4 = s3

h3 = h@P3,T3

h4 = [hf +xhfg]@P4

4P@fg

4P@f3

sss

x

h2 = h1 +2(P2 – P1); where1P@f12

Note that P1 = P4

Review – Ideal Rankine CycleEnergy Analysis

23

1423

in

outin

in

out,net

hhhhhh

qqq

q

Efficiency

23

1243

in

inout

in

out,net

hhhhhh

qq

23

1243

hhhhhh

Review – Reheat Rankine CycleP

ump

Boiler Hig

h P

turbine

Condenser

High T Reservoir, TH

qin = qH

in

out,1

qout = qL

Low T Reservoir, TL

Low P

turbine out,2

1

23

4

5

6

qreheat

Reheating increases and reduces moisture in turbine

Review – Reheat Rankine Cycle

TL= Tsat@P1

in

s5 = s6s1 = s2

Tcrit

TH

Tsat@P4

Tsat@P3

s3 = s4

qout = h6-h1

out, II

P4 = P5

P6 = P1

61

5

4

qreheat = h5-h4

qprimary = h3-h2 outP3

3

2

T, C

s, kJ/kgK

s6 = [sf +xsfg]@P6. Use x = 0.896 and s5 = s6

h6 = [hf +xhfg]@P6

Energy AnalysisReview – Reheat Rankine Cycle

q in = qprimary + qreheat = h3 - h2 + h5 - h4 qout = h6-h1

net,out = out,1 + out,2 = h3 - h4 + h5 - h6

4523

164523

in

outin

in

out,net

hhhhhhhhhh

qqq

q

4523

6543

in

2out1out

in

out,net

hhhhhhhh

qq

Vapor power cycles – Rankine cycleGas Mixtures – Ideal Gases

Water as working fluidcheapEasily availableHigh latent heat of vaporisation, hfg.

Use property table to determine properties

Non-reacting gas mixtures as working fluid

Gas Mixtures – Ideal Gases

Properties depends onComponents (constituents) of mixturesAmount of each componentVolume of each componentPressure each component exerts on container walls

Extended properties may not be tabulated Treat mixture as pure substancesExamples: Air, CO2, CH4 (methane),

C3H8 (Propane)

Ideal GasesGas Mixtures – Ideal Gases

Low density (mass in 1 m3) gases

Molecules are further apart

Real gases satisfying condition

PPgasgas << P << Pcritcrit; T; Tgasgas >> T >> Tcrit crit , have low density and can be treated as ideal gases

High density

Low densityMolecules far apart


Equation of StateEquation of State - P--T behaviour

PP=RT=RT (energy contained by 1 kg mass) where is the specific volume in m3/kg, RR is gas constant, kJ/kgK, TT is absolute temp in Kelvin.

High density

Low densityMolecules far apart



PP=RT=RT , since = V/m then,P(V/m)=RT. So,PV =mRTPV =mRT, in kPam3=kJ.Total energy of a system.

Low density

High density



PV =mRTPV =mRT = NMRT = N(MR)THence, can also write PV = PV = NRNRuuTT whereNN is no of kilomoles, kmol,MM is molar mass in kg/kmole andRRuu is universal gas constant; RRuu=MR=MR. RRuu = 8.314 kJ/kmol = 8.314 kJ/kmolKK

Low density

High density


Equation of StateEquation of State for mixturesPPmixmixmixmix=R=RmixmixTTmixmix , PPmixmixVVmixmix =m =mmixmixRRmixmixTTmixmix PPmixmixVVmixmix = N = NmixmixRRuuTTmixmix where mmmixmix = M = MmixmixNNmixmix

RRmixmix is apparent or mixture gas constant, kJ/kgK,

TTmixmix is absolute temp in Kelvin, NNmixmix is no of kilomoles,MMmixmix is molar mass of mixture in kJ/kmole andRRuu is universal gas constant; RRuu=MR=MR. RRuu = 8.314 kJ/kmol = 8.314 kJ/kmolKK

Composition of gas mixturesGas Mixtures – Ideal Gases

Specify by mass (gravimetric analysis) or volume ( volumetric or molar analysis)

MNm Mass isMass is , in kg, in kg

MmN Number of Number of

kilomoles iskilomoles is, in , in kmolekmole

mass = Molar mass * Number of kilomolesmass = Molar mass * Number of kilomoles

Gravimetric Analysis

Gas Mixtures – Composition by Mass

Composition by weight or massMass of components add to the total mass of mixtures

+

6 kg

H2 O2

32 kg+

= = 38 kgH2 +O2

%8.151579.0386

mm

mfmix

HH

22

Mass fraction of componentsMass fraction of components22 OHmix mmm

%2.848421.03832

mm

mfmix

OO

22

Volumetric Analysis

Gas Mixtures – Composition by Moles

Composition by kilomolesNumber of kilomoles of components add to the total number of kilomoles of mixtures

+

3 kmol

H2 O2

1 kmol+

= = 4 kmolH2 +O2

22 OHmix NNN

22 OHmix Mm

Mm

Mm

MmN Number of kilomoles is

Hence,

Volumetric Analysis


+

3 kmol

H2 O2

1 kmol+

= = 4 kmolH2 +O2

%7575.043

NN

ymix

HH

22

Mole fraction of components

%2525.041

NN

ymix

OO

22

molk 3kmolkg/ 2kg 6N

2H

molk 1kmolkg/ 32kg2 3N

2O

Hence

Composition Summary


+

3 kmol

H2 O2

1 kmol+

= = 4 kmolH2 +O2

Gravimetric Analysismix21 mmm

Volumetric Analysis

100% or 1mfmf 21

mix21 NNN

100% or 1yy 21

mix

ii m

mmf where

mix

ii N

Ny where

Dalton’s LawGas Mixtures – Additive Pressure

PH2

H2 O2

PO2

+

+

= = PH2+ PO2

H2 +O2

The total pressure exerted in a container at volume V and absolute temperature T, is the sum of component pressure exerted by each gas in that container at V, T.

21mix PPP

k is total number of components;)T,(V PPk

1imixmiximix

Amagat’s LawGas Mixtures – Additive Volume

The total volume occupied in a container at pressure Pmix and absolute temperature Tmix, is the sum of component volumes occupied by each gas in that container at Pmix, Tmix. 21mix VVV

;)T,(P VVk

1imixmiximix

k is total number of components

VH2

H2 O2

VO2

+

+

= = VH2+ VO2

H2 +O2

Partial PressureGas Mixtures –Pressure Fraction

The pressure fraction for each gas inside the container is

1mix

1

umix

u1

mix

1 yNN

VTRN

VTRN

PP

mix11 PyP

H2 +O2

Hence the partial pressure is

mixii PyP In general,

;TRNVP mixUmixmixmix Since mixU1mix1 TRNVP

Partial VolumeGas Mixtures –Volume Fraction

The volume fraction for each gas inside the container is

1mix

1

umix

u1

mix

1 yNN

PTRN

PTRN

VV

mix11 VyV

H2 +O2

Hence the partial volume is

mixii VyV In general,

;TRNVP mixUmixmixmix Since mixU11mix TRNVP

thermodynamics lecture series

Documents