chapter 2_fundamental of thermodynamics

8/13/2019 Chapter 2_Fundamental of Thermodynamics

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Thermal Engg.

CHAPTER 2 Fundamentals of Thermodynamics

ThermodynamicsIt is the science that deals with heat and work.

Heat EngineA machine, which converts heat into mechanical work or vice versa, is known asHeat Engine. The working substance widely used in heat engines are in gaseous orliquid state. eg. IC engines - miture o! air and !uel, Turbine " steam.

Concepts of Pure SubstanceA #ure substance is a single substance which retains an unvarying molecularstructure during the #rocess o! energy trans!er. A #ure substance eists in three#hases namely gaseous, liquid and solid, maintaining its chemical com#osition. Asystem o! ice, water and steam may be considered to be a #ure substance, since the

molecular structure in all three #hases remains same. Also, a system that includesany chemical #rocess, such as combustion would not be a #ure substance duringthe #rocess because the molecular structure be!ore and a!ter the #rocess aredi!!erent.Significance

Any #articular condition or state o! a #ure !luid at rest is com#letely de!ined by two

inde#endent #ro#erties.

It is use!ul in determining the #ro#erties o! a working substance at various

conditions o! #ressure and tem#erature.

It is also convenient in the #re#aration o! charts and tables o! #ro#erties to be

used in the design o! equi#ments using the #ure substance as working medium.

Types of System

A thermodynamic systemis de!ined as a region in s#ace or a quantity o! matter

u#on which attention is !ocussed !or the study o! work and energy trans!er andconversion.

Everything outside the system which has direct bearing on its behaviour is known

as surroundings. The system is se#arated !rom the surroundings by the systemboundarywhich can be !ied or movable.

$ass and energy trans!er takes #lace between the system and surroundings

through the boundary o! the system.

%hen system and surrounding are #ut together, it is called universe

A !ied region in s#ace through which mass and energy !low takes #lace is called

control volume

&

'('TE

)*+A(

'+*+I

$*/A)0E)*+A

1I2E)*+A

3I'T*

C(0IE


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Thermal Engg.

The sur!ace o! control volume is called control surface

The di!!erent ty#es o! systems are

! Closed System

An eam#le o! a closed system is #iston and cylinder.

The mass o! the closed system remains constant and only energy can !lowthrough the boundary in or out o! a closed system.

The volume o! a closed system need not be constant and it changes due to the

movement o! the #iston in the cylinder.

%ork trans!er between system and surroundings takes #lace due to the

movement o! the boundary o! the system considered.

*ther eam#le is thermal #ower #lant.

2 "pen System

An eam#le o! an o#en system is turbine, boiler, air com#ressor etc.

$ass, heat and energy trans!er takes #lace through the boundary o! an o#en

system. The boundary during the trans!er o! mass and energy may change or may not

change.

It can be described with the hel# o! control volume and control sur!ace.

# $solated System

An eam#le is gas enclosed in a insulated vessel.

A system which is com#letely unin!luenced by the surrounding is an isolated

system.

It a system o! !ied mass and no heat, mass or energy cross its boundary.

4

5A'

3I'T* 6

C(0IE

3I'T*

C(0IE

%

%

'TEA$

C*T*0

C*T*

0

'TEA$

5A' I'+0ATI*


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Thermal Engg.

State of a System

'tate can be de!ined as eact condition o! the system.

The state can be de!ined by thermodynamic #ro#erties such as #ressure,tem#erature, volume etc.

At least two #ro#erties are necessary to de!ine the state o! system.

Thermodynamic E%uilibriumA system is said to be in thermodynamic equilibrium, i! it satis!ies the !ollowing threerequirements o! equilibriuma &echanical E%uilibrium A system is said to be in mechanical equilibrium, when there is no unbalance

!orces acting on any #art o! the system or the system as a whole.

b Thermal E%uilibrium A system is said to be in thermal equilibrium, when there is no tem#eraturedi!!erence between the #arts o! the system or between the system and thesurroundings.

c Chemical E%uilibrium A system is said to be in chemical equilibrium, when there is no chemical reaction

within the system and no reaction with surroundings.

Thermodynamic Process%hen a system changes its state !rom one equilibrium state to another then the #atho! successive states through which the system has #assed is known as

thermodynamic #rocess. 3rocess &-4 re#resents a thermodynamic #rocess.

Thermodynamic Cycle or Cyclic Process%hen #rocesses are #er!ormed on a system in such a way that the !inal state isidentical with the initial state then it is known as thermodynamic cycle or cyclic

#rocess. &-A-4 and 48& are #rocesses whereas &-A-4-)-& is cycle or cyclic #rocess.

Reversible ProcessI! a #rocess occurs in such a way that the system #asses through a continuousseries o! equilibrium states, then such a #rocess is called reversible #rocess. It canbe shown by a well de!ined curve on two dimensional thermodynamic diagram.

9

/

3

/

&

4

3

&

4A

)


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Thermal Engg.

$rreversible ProcessI! a system does not #ass through equilibrium states then the #ro#erties at theintermediate states o! the system cannot be re#resented on two dimensionalthermodynamic diagram. The #ath o! such irreversible #rocess between the twostates is always re#resented by a dotted line as the #ath !ollowed is uncertain.

$rreversibilityAny #rocess that is not reversible is known as an irreversible #rocess. All natural#rocesses ie s#ontaneous #rocesses are irreversible. Eg. Trans!er o! heat !rom high

tem#erature to low tem#erature.1actors making #rocess irreversible:a Friction' According to second law work can be entirely converted to heat but heat cannot

be converted to work. %ork lost in !riction cannot be recovered and it makes the#rocess irreversible.

b Free E(pansion' %hen gas e#ands !reely it is not #ossible to bring it to initial stage without

a##lication o! work. Thus #rocesses become irreversible.c Heat transfer through finite temperature difference' Heat !lows s#ontaneously !rom high tem#erature to low tem#erature but to reverse

the #rocess eternal work is to be done. This makes the #rocess irreversible.

Properties of SystemAny characteristic o! the substance which can be observed or measured is called a#ro#erty o! the substance. The basic #ro#erties o! system are volume, #ressure,tem#erature etc. There are two ty#es o! #ro#erties vi; &.?&9 &?@=m4 ?r F? mm o! Hg at sealevel.

,olume ),*It is the s#ace occu#ied by a substance. Its unit is m9or litres.

Specific ,olume )v*It is de!ined as volume #er unit mass. Its unit is m9=kg.

v >m

V

-ensity ).*It is de!ined as the mass #er unit volume o! a substance. Its unit is kg=m9.

G >V

m

Temperature )T*

It is an intensive thermodynamic #ro#erty, which determines the degree o! hotnesso! a body. Tem#erature is measured by thermometer and thermocou#le. The twoscales used !or measuring the tem#erature are Celsius or Centigrade CB or1ahrenheit 1B.Each o! these scales is based on two !ied #oints known as !ree;ing #oint o! waterunder atmos#heric #ressure or ice #oint and the boiling #oint o! water or steam #oint.Celsius or Centigrade )/C*1ree;ing #oint o! water is marked as ? and boiling #oint is marked as &??. Thes#ace between these two #oints has &?? equal divisions each re#resenting & C.Fahrenheit )/F*1ree;ing #oint o! water is marked as 94 and boiling #oint is marked as 4&4. The

s#ace between these two #oints has &? equal divisions each re#resenting & 1.Conversion

@

A)'*0+

TE

5A+5E

/AC++$

A)'*0+

TE

3E''+E A)*/E AT$*'3HEIC

AT$*'3HE

IC

3E''+E

)E0*%

AT$*'3HEIC

A)'*0+TE JE*


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Thermal Engg.

180

32

100

=FC

Absolute TemperatureThe tem#erature, below which the tem#erature o! any substance cannot !all, is

known as absolute ;ero tem#erature. Absolute ;ero is taken as - 49 C or - F? 1.It is called degree Kelvin in Celsius scale such that K > C D 49. And degreerankine in 1ahrenheit scale > 1 D F?.

EnergyIt is de!ined as the ca#acity to do work. The energy #ossessed by a system is o! the!ollowing two ty#es:! Stored Energy

It is the energy #ossessed by a system within its boundaries. The #otentialenergy, kinetic energy and internal energy are eam#les o! stored energy.

2 Transit Energy

It is the energy #ossessed by a system which is ca#able o! crossing itsboundaries. The heat, work and electrical energy are eam#les o! transit energy.

'tored energy is a thermodynamic #ro#erty whereas the transit energy is not athermodynamic #ro#erty as it de#ends u#on the #ath.

Stored EnergyPotential Energy )PE*It is the energy #ossessed by a body due to its #osition above ground level or anyre!erence level. Its units are -m or Loules. 3E > mgh%here m > mass o! the body g> acceleration due to gravity > M.& m=s4 h > distance through which the body !alls

0inetic Energy )0E*It is the energy #ossessed by a body or a system !or doing work due to its mass andvelocity o! motion. Its units are -m or Loules.

KE >2

1 m/4

%here / > velocity o! body m > mass o! the body

$nternal Energy )1*It is the energy #ossessed by a body or a system due to its molecular arrangementand motion o! the molecules. In thermodynamics, we are concerned with the changein internal energy d+B which de#ends u#on the change in tem#erature o! thesystem.The total energy o! the system E > 3EDKED+%hen the system is stationary and the e!!ect o! gravity is neglected then 3E>KE>?Hence E> +

or e>u !or unit massB

F


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Thermal Engg.

Transit EnergyHeat )*It is de!ined as the energy trans!erred across the boundary o! a system because o!tem#erature di!!erence between the system and the surroundings. Its unit is LouleLB.

'ign convention:Heat !lowing into a system is #ositive

Heat !lowing out o! a system is negative

Specific Heat )C*It is de!ined as the amount o! heat required to raise the tem#erature o! a unit mass o!any substance through one degree. Its unit is kL=kgK.'ince the solids and liquids do not change in volume on heating, there!ore they have

only one s#eci!ic heat. )ut the gases have two s#eci!ic heats de#ending on the#rocess ado#ted !or heating the gas.'#eci!ic heat at constant volume CvB'#eci!ic heat at constant #ressure C#BC#is always greater than Cv.

Thermal or Heat CapacityHeat ca#acity o! a substance may be de!ined as the heat required to raise thetem#erature o! whole mass o! a substance through one degree. Its unit is kL.Heat Ca#acity > mC kLm > mass o! the substance in kg.C > s#eci!ic heat o! the substance in kL=kgK.

3or4 )3*%ork is said to be done by a system during a given o#eration i! the sole e!!ect o! thesystem on things eternal to the system surroundingsB can be reduced to the raisingo! a weight.

%> 1 d%here, 1 > !orce d > distanceThe work done by the system is #ositive work

The work done on the system is negative work.

-ifference bet5een 5or4 and heat3or4 Heat

&. It is the #roduct o! !orce and dis#lacement &. It is de!ined as the energytrans!erredin the direction o! !orce. across the boundary o! a system

because o! tem#erature di!!erencebetween the system and thesurroundings.

4. %ork is high grade energy. 4. Heat is low grade energy.9. Entire work can be converted to heat. 9.Entire heat cannot be converted to

7 Dve

7 -ve


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Thermal Engg.

work.. %ork done by the system is #ositive and . Heat received by the

system iswork done on the system is negative. #ositive and heat reNected bythe

system is negative.

Flo5 Energy or Flo5 3or4 )FE*It is de!ined as the work necessary to advance a !luid against the eisting #ressure.1low energy > 1orce distance > 3 A Ol > 3 /

Enthalpy )H*It is the total heat content o! the system and is de!ined as the sum o! internal energyand !low work. It units are kL=kg.

H > + D 3/

Entrophy )S*It is thermodynamic #ro#erty o! system which increases with addition o! heat anddecreases with removal o! heat. Its unit are kL=K.

O' >T

dQ

%here, d7> heat absorbed or heat reNected, T> Absolute Tem#erature, O'> change in entro#y

Point Function3oint 1unction has single value at each state o! the system. They de#end on thestate o! the system. Eg #ressure, tem#erature, volume etc.

2

1dV > /4- /&

/olume does not de#end on #ath.

Path FunctionThe thermodynamic quantities which are de#endent on the #ath !ollowed betweenthe two states o! the #rocess are #ath !unctions. eg. %ork and heat.

2

1

dW %&" %4

/

/

3ath A

3

&

4

3ath )

3

&

4


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Thermal Engg.

3or4 and Heat 6 A Path FunctionWork

The work done during the #rocess !rom state & to state 4 is re#resented by areaunder the curve &-4. It is #ossible to go !rom state & to state 4 along many #athssuch as A, ) or C. 'ince area under each curve re#resents work !or each #rocess it

is evident that work is de#endent o! #ath that is !ollowed. That is why work is called a#ath !unction.

%&-4> 1

2

V

VPdV

Heat

Area under a T' diagram gives the heat trans!er. There!ore heat is also a #ath

!unction. It de#ends on the #ath the system has !ollowed !rom & to 4.7&-4>

2

1Tds

All #ro#erties o! a system are #oint !unction ie stored energy 3E, KE, +B are #oint!unctions but transit energy ie heat and work are #ath !unction.7a5s "f Thermodynamic

8eroth 7a5 "f ThermodynamicsThis law states P%hen two systems are each in thermal equilibrium with a thirdsystem, then the two systems are also in thermal equilibrium with one anotherQ.This law #rovides basis !or tem#erature measurement. eg. A thermometer is used tocom#are the tem#erature o! the body o! unknown thermal level with the tem#eratureo! the body at a known thermal level.

!st7a5 of Thermodynamics )Conservation of energy*This law states that PThe energy can neither be created nor destroyed but it can betrans!ormed !rom one !orm to anotherQ.1or a closed system, heat and mechanical work are mutually convertible ie net heat

trans!er is equal to the net work trans!er. In other words, the cyclic integral o! heattrans!ers is equal to the cyclic integral o! work trans!ers.

= WQ stands !or integral around a com#lete cycleB%hen a system undergoes a change o! state, then both heat trans!er and worktrans!er takes #lace. The net energy trans!er is stored within the system and isknown as stored energy or total energy o! the system.R7 " R% > dE

M/3

s

//

%&-4

C3

&

4A

)

3

/3

&

4

7&-4

3

&

4

%*K

T

&

4

C(C0IC

3

&

43*CE'


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Thermal Engg.

*n integrating !or a change o! state !rom & to 4, we get 7&-4" %&-4> E4" E&%here, 7&-4 > Heat trans!erred to the system during the #rocess !rom state & to state

4, %&-4> %ork done by the system on the surroundings during the #rocess E& > Total energy o! the system at state & > 3E&D KE&D +&

E4 > Total energy o! the system at state 4 > 3E4D KE4D +41or non !low thermodynamic system or closed system there is no change o! 3E andKE 7&-4" %&-4> +4" +& > d+1or an isolated system 7&-4> %&-4> ?, E4> E&

Application of !st7a5 of ThermodynamicsSteady Flo5 System'a. The mass !low rate through the system remains constant.b. There is no change in chemical com#osition o! the !luid or there is no chemical

reaction.c. The state o! !luid at any #oint remains constant with time.d. 1luid is uni!orm in com#osition.e. The only interactions between the system and surroundings are work and heat

and they are constant.!. The #otential, kinetic, internal and !low energies are only considered in the

analysis. *ther !orms o! energy electrical, chemical, magnetic etc.B are notconsidered.

Consider & kg o! mass o! working !luid enters in the system at & and leaves thesystem at 4. 0et the energy at entry and eit be & and 4 res#ectively.As #er &stlaw o! thermodynamicsq&-4" w&-4 > e4" e& ----------------- equation &Total energy e&entering the system #er kg at entry &e& > 3E&D KE&DInternal Energy D 1low %ork

> g;&D

2

1v&

4 D u& D3&/& ---------------- equation 4

Total energy e4eiting the system #er kg at eit 4e4 > 3E4D KE4DInternal Energy D 1low %ork

> g;4D2

1v4

4D u4D34/4 -------------- equation 9

%here, g > acceleration due to gravity > M.& m=sec;&, ;4> elevation above ground level at enter and eit res#ectively,v&, v4> velocity o! !luid at enter and eit res#ectively,u&, u4> internal energy o! !luid at enter and eit res#ectively,3&, 34> 3ressure o! !luid at enter and eit res#ectively,/&, /4> /olume at enter and eit res#ectively,

earranging equation &, 4 and 9 we get,

&?

q&-4;

;

w&-4

I0E

*+T0E

'('TE


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Thermal Engg.

q&-4 " w&-4 > Sg;4D2

1v4

4D u4D34/4 - Sg;&D2

1v&

4D u&D3&/&

A!ter rearranging

q&-4 D g;&D2

1v&

4D h& > w&-4 D g;4D2

1v4

4D h4

This is steady !low energy equation.

Application of Steady Flo5 Energy E%uation! 9oiler' It is a device which su##lies heat to water and generate steam.&. o change in KE and 3E4. o work done

A##lying '1EE

g;&D2

1v&

4D h&D q&-4> g;4D2

1v4

4D h4D w&-4

q&-4 > h4- h&Heat su##lied to the boiler increases enthal#y o! system.

2 CondenserA condenser is a device used to condense steam in steam #ower #lants usingwater as cooling medium whereas in re!rigeration system air is used as coolingmedium to condense re!rigerant va#our.

&. o change in KE and 3E4. o work done

A##lying '1EE

g;&D2

1v&

4D h&- q&-4> g;4D2

1v4

4D h4D w&-4

q&-4> h&- h4

q&-4 is negative as heat is lost by working !luid.

# :o;;leThis is a device which increases the velocity o! working !luid at the e#ense o!#ressure dro#. The no;;le is insulated so that no heat enters or leaves the

system.&. o heat trans!er4. o work done by the system9. o change in 3E

A##lying '1EE

g;&D2

1v&

4D h&D q&-4> g;4D2

1v4

4D h4D w&-4

h&- h4>2

1S v4

4-v&4

I! v&is small, it can be neglected

v4> )21(2 hh

&&

q&-4

%ATE

'TEA$

)*I0E

I0ET

*+T0E

C*/E5 I/E5E


12/26

Thermal Engg.

g;4D2

1v4

4D h4- w&-4

w&-4> h4 - h& D q&-4> Evaporator

It is a device used in re!rigeration

system in which liquid receives heat andleaves as va#our.&. o work done by the system4. o change in KE and 3EA##lying '1EE

g;&D2

1v&

4D h&D q&-4> g;4D2

1v4

4D h4D w&-4

q&-4> h4-h&

:ote'%ork and heat are not com#letely interchangeable !orms o! energy. %ork is

said as high grade energy while heat is low grade energy. Com#lete conversion !romlow grade to high grade in a cycle is im#ossible.

7$&$TAT$":S "F F$RST 7A3 "F THER&"-?:A&$CS&. The law does not s#eci!y the direction o! !low o! heat and work.4. It also does not give any condition under which these trans!ers take #lace.9. Though the mechanical work can be !ully converted into heat energy, but only a

#art o! heat energy can be converted into mechanical work.

Perpetual &otion &achine $ )P&&@$*A machine which violates the !irst law o! thermodynamics is known as 3$$ I. It is

de!ined as a machine which #roduces work energy without consuming an equivalento! energy !rom other sources. It is im#ossible to obtain such a machine.

&4

0iquide!rigerantIn

w&-4

5A' *

5A' * 'TEA$

T+)I

I'+0ATI*

q&-4

/a#oure!rigerant*ut


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Thermal Engg.

E:ER+? RESER,"$RA thermal energy reservoir is de!ined as large body o! in!inite heat which is ca#ableo! absorbing or reNecting an unlimited quantity o! heat without a!!ecting itstem#erature.

i S"1RCEThe thermal energy reservoir !rom which heat is trans!erred to the systemo#erating in a heat engine cycle is called the source. Eg: the sun, a constanttem#erature !urnace where !uel is continuously burnt.

ii S$:0The thermal energy reservoir to which heat is reNected !rom the system during a

cycle is called the sink. Eg: river, sea or atmos#here

SEC":- 7A3 "F THER&"-?:A&$CSIt is commonly de!ined in two ways Kelvin 3lanck and Clausius statements:

! 0elvin Planc4 Statement'It is im#ossible to construct an engine working on a cyclic #rocess, whose sole#ur#ose is to convert heat energy !rom a single thermal reservoir into anequivalent amount o! work.

In other words, no actual heat engine, working on a cyclic #rocess, can convertwhole o! the heat su##lied to it into mechanical work. It means that there is adegradation o! energy in the #rocess o! #roducing mechanical work !rom theheat su##lied.

Perpetual &otion &achine $$ )P&&@$$*A heat engine which violates the second law is known as #er#etual motion machineo! 4ndkind. It converts whole o! heat energy into mechanical work. It is a &?? Ue!!icient machine which is im#ossible in actual #ractice.

Application of second la5 to heat engines1or the satis!actory o#eration o! heat engine there should be atleast two reservoirs o!heat one at a higher tem#erature and one at a lower tem#erature.

&9


14/26

Thermal Engg.

ma > pliedHeatobtainedworkimum

sup

max>

1

21

Q

QQ

>1

21

T

TT heat engineB

2 Clausius StatementIt is im#ossible !or a sel! acting machine, working in acyclic #rocess, to trans!erheat !rom a body at a lower tem#erature to a body at a higher tem#eraturewithout the aid o! an eternal agency.

In other words, heat cannot !low itsel! !rom a cold body to a hot body without thehel# o! an eternal agency without the e#enditure o! mechanical workB.

Perpetual &otion &achine $$ )P&&@$$*The device such as a re!rigerator or a heat #um# violates the Clausius statementbecause no in#ut work is su##lied to the device to trans!er heat !rom a cold body to ahot body. 'uch a device is called #er#etual motion machine o! the second kind.

Application of second la5 to refrigerator and heat pump RefrigeratorIt is a device which o#erating in a cyclic #rocess, maintains the tem#erature o! a cold

body re!rigerated s#aceB at a tem#erature lower than tem#erature o! thesurrounding.

&


15/26

Thermal Engg.

Though the body will be insulated there will be always heat leakage 7 4into the body!rom surrounding due to tem#erature di!!erence. In order to maintain cold body attem#erature T4, heat is to be removed !rom the body at same rate at which the heatis leaking in same body.The #er!ormance o! re!rigerator is measured in terms o! co e!!icient o! #er!ormancewhich is de!ined as ratio o! desired e!!ect to the work required to #roduce it.

C*3 > quiredWork

EffectDesired

Re>

21

2

QQ

Q

>21

2

TT

T

Heat PumpIt is a device which o#erating in a cyclic #rocess, maintains the tem#erature o! a hotbody heated s#aceB at a tem#erature higher than the tem#erature o! surroundings.

The body will be maintained at T&i! heat is su##lied to it at same rate at which it isleaking out o! the body. The heat is etracted !rom low tem#erature reservoiratmos#hereB and discharged into high tem#erature body by work in#ut.

&@


16/26

Thermal Engg.

C*3# > quiredWork

EffectDesired

Re>

21

1

QQ

Q

>21

1

TT

T

>21

221

TTTTT

+> &D

21

2

TTT

adding and subtracting T4B

> &D C*3

C*3 o! a heat #um# is greater than C*3 o! a re!rigerator by unity.

Also, a re!rigerator works between the cold body tem#erature and the atmos#herictem#erature hot bodyB whereas a heat #um# o#erates between the hot bodytem#erature and the atmos#heric tem#erature cold bodyB.

E%uivalence of 0elvin@Planc4 and Clausius StatementsKelvin-3lanck and Clausius statement are virtually equivalent in all res#ects. Theequivalence can be #roved i! violation o! Kelvin-3lanck statement im#lies theviolation o! Clausius statement and vice versa.

&. /iolation o! Kelvin- 3lanck 'tatement:

Consider a system, a heat engine having &?? U thermal e!!iciency ie 3$$ IIB

is violating the Kelvin-3lanck statement as it converts the heat energy 7 &B

&F


17/26

Thermal Engg.

!rom a single high tem#erature reservoir at T &, into an equivalent amount o!work ie %> 7&B.This work out#ut o! the heat engine can be used to drive a heat #um# orre!rigeratorB which receives an amount o! heat 74 !rom a low tem#eraturereservoir at T4and reNects an amount o! heat 7&D74B to a high tem#erature

reservoir at T&. I! the combination o! a heat engine and a heat #um# orre!rigeratorB is considered as a single system, then the result is a device thato#erates in a cycle and has no e!!ect on the surroundings other than thetrans!er o! heat 74 !rom a low tem#erature reservoir to a high tem#eraturereservoir, thus violating the Clausius statement. Hence, a violation o! Kelvin-3lanck statement leads to a violation o! Clausius 'tatement.

4. /iolation o! Clausius 'tatementConsider a system, a heat #um# or re!rigerator ie 3$$ IIB is violating theClausius statement as it trans!ers heat !rom a low tem#erature reservoir at T 4toa high tem#erature reservoir at T&without any e#enditure o! work.

ow let a heat engine, o#erating between the same heat reservoirs, receives anamount o! heat 7&as discharged by the heat #um#B !rom the high tem#eraturereservoir at T&, does work %E> 7&-74B and reNects an amount o! heat 74to thelow tem#erature reservoir at T4. I! the combination o! the heat #um# orre!rigeratorB and the heat engine is considered as a single system, then theresult is a device that o#erates in a cycle whose sole e!!ect is to remove heat atthe rate o! 7&-74B and convert it com#letely into an equivalent amount o! work,thus violating the Kelvin-3lanck statement. Hence, a violation o! Clausiusstatement leads to a violation o! Kelvin-3lanck statement.

&

HI5H TE$3EAT+EE'E/*I AT T&

7

7

0*% TE$3EAT+EE'E/*I AT T4

H

7

7

%> 7&-

0*%

TE$3EAT+E

H

7&- 74

%> 7&-


18/26

Thermal Engg.

Problems on SFEE'&. The velocity and enthal#y o! !luid at inlet o! certain no;;le are @? m=sec and

4?? kL=kg. The no;;le is hori;ontal and insulated so that no heat trans!er takes#lace !rom it. 1ind

a. /elocity o! !luid at eit o! the no;;le.b. $ass !low rate i! area at inlet o! no;;le is ?.?M m4and the s#eci!ic volume is

?.&@ m9=kg.c. Eit area o! no;;le i! s#eci!ic volume at eit o! no;;le is ?.M@ m9=kgEnthal#y at eit is 4F?? kL=kg.5iven:/&> @? m=sec , h&> 4?? kL=kg, h4> 4F?? kL=kg, A&> ?.?M m

4, v&> ?.&@ m9=kg

v4> ?.M@ m9=kg, q&-4> ?, w&-4> ?

1ind:

/4, , A4'olution:A##lying '1EE

g;&D2

1/&

4D h&D q&-4> g;4D2

1/4

4D h4D w&-4

h&- h4>2

1S /4

4-/&4

/4> F9.9 m=sec> G &/&A&> G4/4A4

>1

11

AV

>185.0

09.050

> 4.94 kg=sec

>2

22

AV

4.94 >495.0

43.6342

A

A4 > ?.?&M m

4

4. In a gas turbine gases !low at a state o! @ kg=sec. The gases enter the turbine ata #ressure o! bar with velocity o! &4? m=sec and leaves at a #ressure o! 4 barwith velocity 4@? m=sec. The turbine is insulated. I! enthal#y o! the gas at inlet isM?? kL=kg and outlet is F?? kL=kg determine ca#acity o! turbine.5iven:> @ kg=sec, 3&> bar, /&> &4? m=sec, 34> 4 bar, /4> 4@? m=sech&> M?? kL=kg, h4> F?? kL=kg, q&-4> ?, 3E > ?1ind:Ca#acity o! turbine

'olution:

&


19/26

Thermal Engg.

A##lying '1EE

g;&D2

1/&

4D h&D q&-4> g;4D2

1/4

4D h4D w&-4

w&-4 >2

1/&

4D h&" S2

1/4

4D h4

w&-4 > [email protected]@ kL=kg

Ca#acity o! turbine > w&-4 > @ [email protected]@ &?9

> &9M.@ kL=sec

Problems on 2nd7a5'&. An engine works between the tem#erature limits o! &@ K and 9@ K. %hat

can be the maimum thermal e!!iciency o! this engineV5iven:T&> &@ KT4> 9@ K1ind : math

'olution:

math>1

21

T

TT

>1775

3751775

> . U

4. Cold storage is to be maintained at -@ C while the surrounding is at 9@ C.The heat leakage !rom the surrounding into the cold storage is 4M k%. Theactual C*3 o! the re!rigeration #lant is estimated to be 4Mk%. The actual C*3is &=9rdo! ideal #lant working between same tem#eratures. 1ind the #owerrequired to drive the #lant.5iven:T&> 9@ C > 49D9@ > 9? KT4> -@ C > 49-@ > 4F K74> 4M k%

C*3Bactual>3

1C*3Bideal

1ind: %'olution:

C*3Bideal>21

2

TT

T

>

268308

268

> F.

C*3Bactual>3

1C*3Bideal>

3

1 F.

> 4.49

&M

'*+CET&> &@ k

'IKT4> 9@ k

H

7

7

%> 7&-

'+*+I5T&> 9? k

C*0'T*A5E

7

7

%> 7&-


20/26

Thermal Engg.

C*3Bactual>W

Q2>

23.2

29

% > &4.M k%

9. A machine o#erating between 9? K and 4F? K. etermine the C*3 when it iso#erated as re!rigerator machine and heat #um#. raw block diagrams.5iven:T&> 4F? KT4> 9? K

1ind: C*3BH3, C*3B

C*3B>21

2

TT

T

>

30260

30

> ?.&9?

C*3BH3>21

1

TT

T

>

30260

260

> &.&9?

. The higher and lower tem#erature in a re!rigerator working on a reversedcarnot cycle are 9@ C and -&@ C. Ca#acity o! machine is 9@.&F k%. 1indC*3, #ower to run and heat reNected !rom system.5iven:T&> 9@ C > 49D9@ > 9? K

T4> -&@ C > 49-&@ > 4@ K74> 9@.&F k%1ind:C*3B, %, 7&'olution:

C*3B>21

2

TT

T

>

258308

258

> @.&F

C*3B>W

Q2>

16.5

16.35

% > F.& k%

7&> %D 74> F.& D 9@.&F > &.M k%

@. An engineer claims that its re!rigeration gives C*3 at F while workingtem#erature limit o! 9@ C and -&@C. Lusti!y the claim.

5iven:T&> 9@ C > 49D9@ > 9? KT4> -&@ C > 49-&@ > 4@ K

C*3Bactual> F1ind:

4?

'+*+I5T&> 4F? k

C*0'T*A5E

7

7

%> 7&-

'+*+I5T&> 4F? k

C*0'T*A5E

H

7

7

%H3> 7&- 74

'+*+I5

T&> 9? k

C*0'T*A5E

7

74> 9@.&F

%> 7&-

'+*+I5T&> 9? k

C*0'T*A5E

7

%> 7&-


21/26

Thermal Engg.

C*3Bideal'olution:

C*3Bideal>21

2

TT

T

>

258308

258

> @.&F

An ideal cycle will have C*3 o! @.&F so actual C*3 cannot bemore than ideal. 'o the claim is !alse.

F. The C*3 o! re!rigerator o#erating on carnot cycle is @. and it maintains -@C inthe eva#orator. Calculate the condenser tem#erature and re!rigeration e!!ect i!#ower required to drive the unit is @ k%.

5iven:%> @ k%T4> -@ C > 49-@ > 4F K

C*3B> @.1ind:T&, 74'olution:

C*3B>21

2

TT

T

@. >268

268

1 T

T& > 9&.F9 K

C*3B>W

Q2

74 > @. @ 74 > 4 k%

. A re!rigerator o#erates between ?C and -4@C. Ca#acity is &4 tons. 1ind C*3,#ower required and heat reNected.

5iven:T&> ? C > 49D? > 9&9 KT4> -4@ C > 49-4@ > 4 K74> &4 tons& ton > 9.@& k%1ind:C*3B, %, 7&'olution:

C*3B>21

2

TT

T

>

248313

248

> 9.&@

4&

74

'+*+I5T&

C*0'T*A5E

7

74

%> @

'+*+I5T&> 9&9 k

C*0'T*A5E

7

74> 4.4?

%> 7&-


22/26

Thermal Engg.

C*3B>W

Q2>

815.3

20.42

% > &&.?F9 k%7&> %D 74> &&.?F9 D 4.4?

> @9.4F k%

. A domestic !ood !ree;er is to be maintained at tem#erature o! -&@ C. Theambient air tem#erature is 9? C. I! the heat leaks into !ree;er at the continuousrate o! &.@ kL=s. 1ind the #ower required to #um# this heat out continuously.5iven:T&> 9? C > 49D9? > 9?9 KT4> -&@ C > 49-&@ > 4@ K74> &.@ kL=s1ind:

C*3B, %,'olution:

C*3B>21

2

TT

T

>

258303

258

> @.9

C*3B>W

Q2>

73.5

75.1

% > ?.9?@ kL=s

M. A cyclic heat engine o#erates between a source tem#erature o! ?? C and sinktem#erature o! 9?C. %hat is the least rate o! heat reNection #er k% net out#ut o!an engineV5iven:T&> ?? C > 49 D ?? > &?9 KT4> 9? C > 49 D 9? > 9?9 K% > & k%1ind :74

'olution:

th>1

21

T

TT

>1073

3031073

> &.F U

th>1

21

Q

QQ >

1Q

W

7&> &.9M k%

74> 7&- % > ?.9M k%

44

'+*+I5T&> 9?9 k

C*0'T*A5E

7

74>&.@

%> 7&-

'*+CET&> &?9 k

'IKT4> 9?9 k

H

7

7

%> 7&-


23/26

Thermal Engg.

CHAPTER 2 Fundamentals of Thermodynamicsuestions From Previous 9oard Papers

&. e!ine PEtensive #ro#ertyQ. 5ive two eam#le.$ay ? 4B

i!!erentiate between intensive and etensive #ro#erty. 5ive two eam#les o!each.

$ay &? ec ?B

e!ine intensive #ro#erty and etensive #ro#erty o! the system. 5ive one eam#le

o! each. $ay &44B

4. e!ine a thermodynamic system. i!!erentiate between o#en, closed and isolatedsystem with one eam#le each.$ay ?M $ay ? FB

9. i!!erentiate between o#en and closed system.$ay &? FBE#lain closed and o#en system. 5ive two eam#les o! each.ec && B

. e!ine system. 0ist its di!!erent ty#es. ec ?M4B

e!ine system and give its classi!ication with eam#les.$ay && B

49


24/26

Thermal Engg.

@. i!!erentiate between heat and work. $ay &&Be!ine high grade and low grade energy with the hel# o! eam#les.ec && B

F. %hat is #ure substanceV

$ay ?M 4B. e!ine #ro#erty o! system. $ay ?M

4Be!ine thermodynamic #ro#erty. 'tate its ty#es and give two eam#les o! each.

ec ?MB

. e#resent system, surrounding and boundary with suitable eam#le.$ay ?M B

M. e!ine #oint !unction and #ath !unction. $ay &4 $ay &&ec ?M 4Bi!!erentiate between #oint !unction and #ath !unction.

ec &4 B&?.e!ine the !ollowing #rocess: reversible and irreversible #rocess. ec &&

4B&&.Comment on PIn #ractice most o! the #rocesses are irreversibleQ to some etent.

$ay ?FB

&4.E#lain the !actors which make the #rocess irreversible.ec ? B

&9.i!!erentiate between reversible and irreversible #rocess. $ay &4B

&.e!ine entro#y. %hat are the characteristics o! entro#yV ec &&B

&@.e!ine thermodynamic work, give its unit. ec &44B

&F.e!ine enthal#y and write its unit. $ay &44B

&.'tate and e#lain Jeroth law o! thermodynamics. 5ive one eam#le o! it. ec &4 ec ?M

B&.E#lain thermal equilibrium and state ;eroth law o! thermodynamics.

ec ? B

&M.'tate !irst law o! thermodynamics. ec &4 $ay &4 $ay?M B 5ive various statements !or P!irst law o! thermodynamics.Q $ay &&

B4?.%hat are the limitations o! 1irst law o! thermodynamicsV ec &4

B4&.e!ine Jeroth law and Kelvin 3lankQs 'tatement o! second law o!

thermodynamics.$ay &4

$ay &? B44.'tate the two statements o! second law o! thermodynamics. ec &4 ec &&

$ay ? B'tate Kelvin-3lank and Clausius 'tatement o! second law o! thermodynamics.

4


25/26

Thermal Engg.

$ay &4 $ay &&ec ? B

49.%rite steady state energy equation. A##ly it to no;;le.$ay ? B

%rite steady !low energy equation and a##ly it to boiler, o;;le, condenser,

com#ressor and Turbine. $ay &4 ec && $ay &? ec ?M$ay ?M ec ? FB'tate steady !low energy equation. 5ive the meaning o! all #arameters containedin it. A##ly this equation to boiler, o;;le.$ay && B

4.3rove the relation between C*3 o! heat #um# and C*3 o! re!rigeration. $ay4??M B

[email protected]!!erentiate between heat engine and re!rigerator with block diagrams. $ay&& B

4F.i!!erentiate between heat #um# and re!rigerator. $ay &?B

4.E#lain the #er!ormance o! a re!rigerator. How is C*3 o! a re!rigeratordeterminedV

ec &&B

4.3rove the equivalence o! Kelvin 3lank statement to Clausius statement. Also#rove the equivalence o! clausius statement to Kelvin 3lank statement.ec && B

4M.E#lain conce#ts o! 3$$ & and 3$$ 4V$ay &4 B

Problems'&. The velocity and enthal#y o! !luid at inlet o! certain no;;le are @? m=sec and 4?? kL=kg.

The no;;le is hori;ontal and insulated so that no heat trans!er takes #lace !rom it. 1inda. /elocity o! !luid at eit o! the no;;le.b. $ass !low rate i! area at inlet o! no;;le is ?.?M m4and the s#eci!ic volume is ?.&@ m9=kg.c. Eit area o! no;;le i! s#eci!ic volume at eit o! no;;le is ?.M@ m9=kg

Enthal#y at eit is 4F?? kL=kg.4. In a gas turbine gases !low at a state o! @ kg=sec. The gases enter the turbine at a

#ressure o! bar with velocity o! &4? m=sec and leaves at a #ressure o! 4 bar withvelocity 4@? m=sec. The turbine is insulated. I! enthal#y o! the gas at inlet is M?? kL=kg andoutlet is F?? kL=kg determine ca#acity o! turbine.

9. A stream o! gases at .@ bar, @?C and &? m=s is #assed through a turbine o! a Net

engine. The stream comes out o! the turbine at 4? bar, @@?C and 4? m=s. The #rocess

is assumed to be adiabatic. The enthal#y o! gas at the entry and eit o! the turbine areM@? kL=kg and F@? kL=kg o! gas res#ectively. 1ind ca#acity o! turbine.

ec &4 B. An engine works between the tem#erature limits o! &@ K and 9@ K. %hat can be the

maimum thermal e!!iciency o! this engineV@. Cold storage is to be maintained at -@ C while the surrounding is at 9@ C. The heat

leakage !rom the surrounding into the cold storage is 4M k%. The actual C*3 o! there!rigeration #lant is estimated to be 4Mk%. The actual C*3 is &=9 rdo! ideal #lant workingbetween same tem#eratures. 1ind the #ower required to drive the #lant.

F. A machine o#erating between 9? K and 4F? K. etermine the C*3 when it is o#erated asre!rigerator machine and heat #um#. raw block diagrams.

. The higher and lower tem#erature in a re!rigerator working on a reversed carnot cycle are

9@ C and -&@ C. Ca#acity o! machine is 9@.&F k%. 1ind C*3, #ower to run and heatreNected !rom system.

4@


26/26

Thermal Engg.

. An engineer claims that its re!rigeration gives C*3 at F while working tem#erature limit o!9@ C and -&@C. Lusti!y the claim.

M. The C*3 o! re!rigerator o#erating on carnot cycle is @. and it maintains -@C in theeva#orator. Calculate the condenser tem#erature and re!rigeration e!!ect i! #owerrequired to drive the unit is @ k%.

ec &4 B&?. A re!rigerator o#erates between ?C and -4@C. Ca#acity is &4 tons. 1ind C*3, #ower

required and heat reNected.&&. A domestic !ood !ree;er is to be maintained at tem#erature o! -&@ C. The ambient air

tem#erature is 9? C. I! the heat leaks into !ree;er at the continuous rate o! &.@ kL=s.1ind the #ower required to #um# this heat out continuously.ec && B

&4. A cyclic heat engine o#erates between a source tem#erature o! ?? C and sinktem#erature o! 9?C. %hat is the least rate o! heat reNection #er k% net out#ut o! anengineV $ay ? B

&9. A re!rigerator works between the tem#erature limits o! -C and 9@C. I! re!rigerator works

on PCarnot CycleQ !ind out its C*3.

$ay && 4B&. A carnot re!rigerator requires &.9 k%=ton o! re!rigeration to maintain the tem#erature o!

4 K. 1ind iB C*3 o! re!rigerator iiB Tem#erature at which heat is reNected. Take & tono! re!rigeration > 9.@& k%B

$ay &4 B

4F

chapter 2_fundamental of thermodynamics

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