INTRODUCTION

1

Course : B.Tech Mechanical

Subject : Elements of Mechanical Engineering

Unit-1

• Prime movers,

• Sources of energy,

• Types of prime movers,

• Force and mass, Pressure, Work, Power, Energy, Heat,

• Temperature, Units of heat, Specific heat capacity,

• Interchange of heat, Change of state,

• Mechanical equivalent of heat, Internal energy, Enthalpy, Entropy, efficiency,

• Statements of Zeroth Law,

• First law and Second Law of Thermodynamics

CONTENTS

• In engineering, a prime mover is an engine that converts fuel to useful work.

• So anything that converts fuel energy into useful work is a prime mover.

PRIME MOVER

• Various energy sources.1. Conventional energy sources– Coil, oil, uranium

2. Non conventional energy sources

– Energies like Solar, wind, biogas and biomass, ocean thermal, geothermal, fuel cells, hydrogen, tidal etc.

SOURCES OF ENERGY

• There are a wide variety of different types of prime movers. Each is designed to use a different type of energy source.

1. Thermal prime movers– E.g. Heat engines

2. Electric power prime movers– Electric motors

3. Hydraulic power prime movers– Turbines

TYPES OF PRIME MOVERS

• Force and Mass:Something which changes or tends to change the state of rest or of uniform motion of a body in a straight line is called force.Its defined by Newton’s second law of motion.Unit is Newton (N)

• Mass is the amount of matter contained in a body.Unit is kg.

BASIC DEFINATIONS

• Pressure:

• Pressure is force per unit area.

P=F/A.

• Its units are atmosphere, bar, Pascal. N/m2.

• A diagram for relation between relative pressure and absolute pressure is shown here.

• Pabs=Patm+Pguage

1

• Units of pressure & its relation:

1 N/m2=1 Pascal

But,1 bar=10^5 Pascal

So, 1 bar=10^5 N/m2

• It can also measured by taking reference of the pressure of Mercury(Hg).

• 1atm=1.01325 bar=760 mm of Hg.

• Work:

A force is said to do work when it acts on a body, and there is a displacement of the point of application in the direction of the force.

i.e, as the bowler throws the ball, he works on ball by applying force.

• It is denoted by W=F*D

here F=force

D=distance covered by object

• Unit of work is Joule.

• Power:

It is known by work done in unit time.

or

Rate of doing work.

P=W/s

• The SI unit of power is watt.

• 1 watt=1 J/s

• Other units are KW, MW, etc.

• Energy:

energy is a property of objects, transferable among them via fundamental interactions, which can be converted in form but not created or destroyed.

• Unit of energy is joule(J).

• Heat:

Simply we can say about heat,

heating is transfer of energy, from a hotter body to a colder one, other than by work or transfer of matter.

It occurs spontaneously whenever a suitable physical pathway exists between the bodies.

• SI unit of heat is also joule(J).

• Temperature:

A temperature is a numerical measure of hot and cold.

or we can say

thermal state of body which distinguishes a hot body from a cold body.

• Main units of temperature is centigrade, Fahrenheit, Kelvin, etc.

• The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.

• Q = m c dT

• Here the product of mass and heat is known as HEAT CAPACITY of substance.

SPECIFIC HEAT

• It is the energy stored in the system.

• Joule’s law of internal energy states that internal energy of perfect gas is only depends on temperature.

• It is denoted by U.

• We can’t measure internal energy but we can find change in it.

INTERNAL ENERGY

• Enthalpy is a defined thermodynamic potential, designated by the letter "H", that consists of the internal energy of the system (U) plus the product of pressure (P) and volume (V) of the system:

H=U+PV

ENTHALPY

• Entropy is a law of nature in which everything slowly goes into disorder.

• The entropy of an object is a measure of the amount of information it takes to know the complete state of that object, atom by atom.

• The entropy is also a measure of the number of possible arrangements the atoms in a system can have. In this sense, entropy is a measure of uncertainty.

ENTROPY

• It can be defined as the ratio of work output to the given work.

• The work we achieve from the system by giving unit work is the Efficiency of system.

EFFICIENCY

• The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then all three are in thermal equilibrium with each other.

ZEROTH LAW OF

THERMODYNAMICS

2

• Energy is neither created nor destroyed, thus the energy of the universe is a constant. However, energy can certainly be transferred from one part of the universe to another.

FIRST LAW OF

THERMODYNAMICS

• CLAUSIUS STATEMENT: It is impossible for a self acting machine working in a cyclic process unaided by any external agency, to convey heat from a body at a lower temperature to a body at a higher temperature.

SECOND LAW OF

THERMODYNAMICS

• KELVIN PLANK STATEMENT: It is impossible to construct an engine, which while operating in a cycle produces no other effect except to extract heat from a single reservoir and do equivalent amount of work.

EXIT

PROPERTIES

OF GAS

The Nature of a Gas:

• have mass

• easy to compress

• have low densities

• fill containers completely

• diffuse quickly (move through each)

• exert pressure (depends on temperature)

Kinetic-Molecular Theory (KMT)

describes the behavior of gases

• A gas consists of very small particles

• The distances between gas particles are relatively large.

• Gas particles are in constant, random motion.

• Collisions between gas particles are perfectly elastic.

• Average KE of particles depends only on the temperature of the gas.

• There is no attractive force between particles of a gas.

Variables That Effect Gases

• Moles (n) – the amount of gas.

• Volume (V) – the size of the container that holds the gas in liters (L).

• Temperature (T) – the speed or kinetic energy of the particles in kelvin (oC +273)

• Pressure (P) – The outward push of gas particles on their container in atmospheres (atm) or millimeters of mercury (mm Hg) or pounds per square inch (psi)

*Think of pressure as the number of collisions between gas particles and their container.

• if P increases, V decreases

• If P decreases, V increases

• If T increases, V increases

• if T decreases, V decreases

• If P increases, T increases

• if P decreases, T decreases

STP – Standard Temperature Pressure

• The behavior of a gas depends on its temperature and the pressure at which the gas is held.

• So far we have only dealt with gases at STP. Standard Temperature and Pressure.

• 273 kelvins and 1 atm.

The Gas Laws

• Boyle’s Law

• Charles’s Law

• Gay-Lussac’s Law

• The Combined Gas Law

• The Ideal Gas Law

Boyle’s Law

• The Pressure-Volume Relationship

• The pressure and volume of a sample of gas at constant temperature are inversely proportional to each other.

(As one goes up, the other goes down)

• P1V1 =P2V2

• If 3 of the variables are known, the fourth can be calculated.

Boyle’s Law

• The gas in a 20.0mL container has a pressure of 2.77atm. When the gas is transferred to a 34.0mL container at the same temperature, what is the new pressure of the gas.

P1V1 =P2V2

2

112

V

VPP

mL

atmmLP

0.34

)77.2(0.202

atmP 63.12

Boyle’s Law

• If a set amount of gas is transferred into a larger container, would the pressure go up or down?

• Would there be more collisions, or fewer collisions with the container holding the gas?

• More volume (space) means fewer collisions with the container, therefore pressure goes down. (From 2.77 atm to 1.63 atm)

Charles’s Law

• The temperature-volume relationship

• At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.

•

2

2

1

1

T

V

T

V

If 3 of the variables are known, the

fourth can be calculated.

Charles’s Law

• What will be the volume of a gas sample at 355K if its volume at 273K is 8.57L?

2

2

1

1

T

V

T

V

1

212

T

TVV

kelvin

kelvinLV

273

)355(57.82

LV 1.112

Charles’s Law

• If the temperature of a given quantity of gas is increased, what will happen to the volume it occupies? (In an elastic container?)

• Gas particles moving faster would have more collisions with the container and exert more force to enlarge the volume of the elastic container.

• In this case, from 8.57L to 11.1L.

Gay-Lussac’s Law

• The Temperature-Pressure Relationship

• If a volume of a sample of gas remains constant, the temperature of a fixed amount of gas is directly proportional to its pressure.

•2

2

1

1

T

P

T

P

If you know 3 of the variables, you can calculate the 4th.

Gay-Lussac’s Law

• The gas left in a used aerosol can is at a pressure of 2.03atm at 25oC. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928oC?

•

•2

2

1

1

T

P

T

P

1

212

T

TPP

K

KatmP

298

)1201(03.22

atmP 18.82

Gay-Lussac’s Law

• If the temperature of a fixed amount of gas goes up, the particles will have more collisions. More collisions means the pressure will increase.

• In this case, when the temp went up the pressure increased from 2.03atm to 8.18atm.

The Combined Gas Law

• If more than one variable changes, a different equation is needed to analyze the behavior of the gas.

•

2

22

1

11

T

VP

T

VP

5 of the variables must be known to calculate the 6th.

The Combined Gas Law

• The volume of a gas-filled balloon is 30.0L at 40oC and 1.75atm of pressure. What volume will the balloon have at standard temperature and pressure?

2

22

1

11

T

VP

T

VP

12

2112

TP

TPVV

)313(00.1

)273)(75.1(0.302

Katm

KatmLV

LV 8.452

The Combined Gas Law

• You have a fixed volume of gas. The temperature decreases which would cause fewer collisions and the pressure decreases which causes fewer collisions as well. What can you do to volume to make the pressure decrease???

• Increase it. More space means fewer collisions.

The Ideal Gas Law

• Describes the physical behavior of an ideal gas in terms of the pressure, volume, temperature and the number of moles of gas.

• Ideal – a gas as it is described by the kinetic-molecular theory postulates.

• All gases are REAL gases… which behave like ideal gases only under most ordinary conditions.

The Ideal Gas Law

• Only at very low temperatures and very high pressures do real gases show significant non-ideal behavior.

• We will assume that gases are close to ideal and that the ideal gas equation applies.

Ideal Gas Equation

PV=nRT

• P-pressure

• V-volume

• n-number of moles of gas

• R-ideal gas constant (universal gas constant) 0.0821 atm.L/mol.K

or 62.396 torr.L/mol.K

• T-temperature

Ideal Gas Equation

• What is the volume occupied by 9.45g of C2H2

at STP?

nRTPV

P

nRTV

First, calculate amount

of gas in moles.

22

2222

03788.261

45.9HgC

HmolCHgCn

223629328.0 HmolCn

Ideal Gas Law

LV 1345217.8

LV 13.8

P

nRTV

atm

kKmolLatmmolV

00.1

273)/0821.0(3629328.0

Ideal Gas Law

• How many moles of a gas at 100oC does it take to fill a 1.00L flask to a pressure of 1.5atm?

RT

PVn

nRTPV

)373(/0821.0

)00.1(5.1

kKmolLatm

Latmn

moln 0490.0

• Internal energy is defined as the energy associated with the random, disordered motion of molecules.

INTERNAL ENERGY

• Cv = du/dT......(1)Cp = dh/dT......(2)

h = u+Pvdh = d(u+Pv) = du+Pdv+ vdp...(3)(3)-->(2)Cp = du+Pdv+ vdp / dT = du / dT+Pdv / dT+ vdp/ dT = Cv+(Pdv + vdp) / dT....(4)For gas ideal, Pv=RT

RELATION BETWEEN Cp & Cv.

• Pdv+vdp = RdT...(5)(5)-->(4)Cp = Cv +RdT/dT = Cv+RCp-Cv = RSo, as temperature change, Cp-Cv will be the same as gas constant, R.

• There are various types of non flow processes just like

1. Reversible constant volume process

2. Reversible constant pressure process

3. Isothermal process

4. Adiabatic process

5. Polytropic process

TYPES OF NON FLOW

PROCESSES

1. Reversible constant volume process

3

2. Reversible constant pressure process

4

3. Iso thermal process

5

3. Iso thermal process

4. Poly-tropic process

6

4. Poly-tropic process

60

EIT

PROPERTIES OF STEAM

• Steam is the vapour or gaseous phase of water

• It is produced by heating of water and carries large quantities of heat within itself.

• Hence, it could be used as a working substance for heat engines and steam turbines.

• It does not obey ideal gas laws but in superheated state it behaves like an ideal gas.

61

• Steam exists in following states or types or conditions.

• (i) Wet steam (mixture of dry steam and some water particles) – evaporation of water into steam is not complete.

• (ii) Dry steam (dry saturated steam) – all water is completely converted into dry saturated steam.

• (iii) Superheated steam – obtained by further heating of dry saturated steam with increase in dry steam temperature.

62

FORMATION OF STEAM

63

7

• ENTHALPY OF STEAM

• Enthalpy of liquid or Sensible heat (hf)

It is the amount of heat required to raise the temperature of one kg of water from 0°C to its saturation temperature (boiling point) at constant pressure. (Line R-S)

hf = cpw (tsat – 0) kJ/kg

cpw = 4.187 kJ/kgK = specific heat of water

• Enthalpy of Evaporation or Latent heat (hfg)• It is the amount of heat required to change the phase of one kg of water from

saturated liquid state to saturated vapour state at constant saturation temperature and pressure. (Line S-T)

• Enthalpy of dry saturated steam (hg)• It is the total amount of heat required to generate one kg of dry saturated

steam from water at

• 0°C. (Line R-S-T)

• hg = hf + hfg

64

Enthalpy of wet steam (h)It is the total amount of heat required to generate one kg of wet steam having dryness fraction x from water at 0°C. It is the sum of sensible heat and latent heat taken by the dry part (x) of the wet steam.h = hf + x(hfg)

Enthalpy of superheated steam (hsup)It is the total amount of heat required to generate one kg of superheated steam at required superheat temperature from water at 0°C. Superheated steam behaves like an ideal gas and obeys gas laws. (Line R-S-T-U)hsup = hf + hfg + cps (Tsup – Tsat)hsup = hg + cps (Tsup – Tsat)cps = 2.1 kJ/KgK = specific heat of superheated steam

Heat of superheatAmount of heat required to get superheated steam from dry saturated steam is called heat of superheat. (Line T-U)Heat of superheat = cps (Tsup – Tsat) kJ/Kg

65

Degree of superheatIt is the temperature difference between superheated steam and dry saturated steam.Degree of superheat = (Tsup – Tsat)

Dryness Fraction of Saturated Steam (x )It is a measure of quality of wet steam. It is the ratio of the mass of dry steam (ms) to the mass of total wet steam (ms+mw), where mw is the mass of water particles in suspension.x = ms/( ms+mw)

Quality of SteamIt is the representation of dryness fraction in percentage: Quality of Steam = 100(x)

Wetness FractionIt is the ratio of the mass of water vapor (mw) to the mass of total wet steam (ms +mw)Wetness fraction = mw/( ms+mw) = (1-x)

PrimingIt is the wetness fraction expressed in percentage.Priming = (1 - x) 100 66

SPECIFIC VOLUME OF STEAMIt is the volume occupied by steam per kg of its mass.

Specific volume of dry steam (vg) : Its value can be obtained directly from the

steam tables

Specific volume of wet steam (v) : v = x (vg)

Specific volume of superheated steam (vsup): vsup = vg (Tsup/Tsat)

INTERNAL ENERGY OF STEAM:

h = u + Pvu = h – PvP = Pressure of steamv = Specific volume of steamug = hg – P(vg) for dry saturated steamu = h – P (v) for wet steamusup = hsup – P(vsup) for superheated steam

67

Calorimeters

Calorimeters are used for measurement of dryness fraction of steam.

Types:

Barrel Calorimeter

Separating Calorimeter

Throttling Calorimeter

Combined Calorimeter

68

Barrel Calorimeter

69

8

• Let• mb =mass of the barrel (kg)• mw =mass of the water before the steam goes in (kg)• ms= mass of stem condensed (kg)• T1= temperature of the water before the steam goes in

(oc)• T2 =temperature of the water after the steam goes in (oc)• Cb= relative heat capacity of the metal of the barrel (no

units)• hf =specific enthalpy of the saturated liquid (steam) (kJ/kg)• hfg =specific enthalpy of the evaporar of steam(kJ/kg)• x =dryness fraction (no units)• hf1= specific enthalpy of the water at temperature T1

(kJ/kg)• Hf2= specific enthalpy of the water at temperature T2

(kJ/kg)

70

• Here known amount of water is filled in the calorimeter. Then certain quantity of steam from the main pipe is taken into the calorimeter.

• Steam and water mixes together and so condensation of steam takes place and mass of water in the calorimeter increases.

• Latent and sensible heat of steam is given to water and its temperature will increase.

71

• Amount of heat lost by steam = Heat gain by water and calorimeter

• ms(hf1+xhfg-hf2)=mb.cb(t2-t1)+mw.cpw(t2-t1)

• =(mb.cb+mwcpw)(t2-t1)

• =((mb × cb)/cpw +mw)(t2-t1)cPW

• (mb × cb)/cpw = water equi. Calorimeter

• Limitation

• 1)method is not accurate

• 2)losses are more at higher temp. diff.

72

Separating Calorimeter

73

9

•In this type of calorimeter water particles from the steam are separated first in the inner chamber and its mass mw can be measured. •The dry steam is then condensed in the barrel calorimeter and its mass ms can be calculated from the difference in mass of water of barrelcalorimeter. •So dryness fraction x = ms/(ms + mw)

•Limitation: It gives approximate value of x as total separation of water particles from the steam is not possible by mechanical means.

74

Throttling Calorimeter

• Throttling

• A throttling process is one in which the fluid is made to flow through a restriction,

• e.g. a partially opened valve or an orifice plate, causing a considerable loss in the pressure of the fluid.

75

76

Throttling Calorimeter

77

10

•In this calorimeter a throttling valve is used to throttle the steam.•The pressure of steam reduces after throttling. Pressure andtemperature of steam before and after throttling is measured.•Enthalpy of steam before and after throttling remains constant.•of water particles.

78

•To measure dryness fraction condition of steam after throttling mustbe superheated steam.•Enthalpy of stem before throttling = Enthalpy of stem after throttling

Limitation: Steam must become superheated after throttling. Thatmeans it is not very useful for steam containing more amount of waterparticles.

79

Combined Separating and Throttling Calorimeter

80

11

•The limitations of separating and throttling calorimeters can beovercome if they areused in series as in this type of calorimeter.•It gives accurate estimation of dryness fraction.

x = x1. x2x1 = dryness fraction of steam measured from separatingcalorimeter.x2 = dryness fraction of steam measured from throttlingcalorimeter.

81

Reference-Sources• Image References

• 1 – http://docs.engineeringtoolbox.com/documents/587/absolute_gauge_pressure.png

• 2 - https://sp.yimg.com/ib/th?id=HN.608050323071501280&pid=15.1&P=0

• 3 -http://upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Isochoric_process_SVG.svg/250px-Isochoric_process_SVG.svg.png

• 4- http://voer.edu.vn/file/55477

• 5- http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/isoth.gif

• 6 - http://mechanical-engineering.in/forum/uploads/blog-0248615001384049799.gif

• 7- http://static.zymergi.com/blog-steam-formation.gif

• 8,9,10,11Elements of Mechanical Engineering by H.G. Katariya, J.P Hadiya, S.M.Bhatt , Books India Publication.

• Content References

• – Elements of Mechanical Engineering by H.G. Katariya, J.P Hadiya, S.M.Bhatt , Books India Publication.

• -Elements of Mechanical Engineering by V.K.Manglik, PHI

• -Elements of Mechanical Engineering by R.K Rajput.

• -Elements of Mechanical Engineering by P.S.Desai & S.B.Soni

Any Question ?

EXIT