The Second Law of Thermodynamics Mp

8/18/2019 The Second Law of Thermodynamics Mp

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The Second Law of Thermodynamics

Due: 8:00pm on Monday, December 12, 2011

Note: You will receive no credit for late submissions. To learn more, read your instructor'sGrading Policy

[!itc" to tandard #ssignment $ie!%

Carnot Cycle: Just How Ideal Is It?

Learning Goal: To understand t"e &uantitatie relations"ips related to ideal ()arnot*engines and t"e limitations o+ suc" deices imposed by t"e second la! o+ t"ermodynamics-n 182., adi )arnot, a /renc" engineer, introduced a theoretical engine t"at "as been sincet"en called a Carnot engine, t"e most e++icient engine possible T"e +ollo!ing statement isno!n as Carnot's theorem: o engine operating bet!een a "ot and a cold reseroir can be more e++icient t"an t"e )arnotengine t"at operates bet!een t"e same t!o reseroirsT"e )arnot engine operates cyclically, ust lie any real engineT"e Carnot cycle includes+our reersible steps: t!o isot"ermal processes and t!o adiabatic ones

-n t"is problem, you !ill be ased seeral &uestions about )arnot engines 3e !ill use t"e+ollo!ing symbols:

• : t"e absolute alue (magnitude* o+ t"e "eat absorbed +rom t"e "ot reseroir during

one cycle or during some time speci+ied in t"e problem4

• : t"e absolute alue (magnitude* o+ t"e "eat deliered to t"e cold reseroir during

one cycle or during some time speci+ied in t"e problem4

• : t"e amount o+ !or done by t"e engine during one cycle or during some time

speci+ied in t"e problem4

• : t"e absolute temperature o+ t"e "ot reseroir4 and

• : t"e absolute temperature o+ t"e cold reseroir

Part A

-n general terms, t"e e++iciency o+ a system can be t"oug"t o+ as t"e output per unit input3"ic" o+ t"e e5pressions is a good mat"ematical representation o+ e++iciency o+ any "eatengine6

http://session.masteringphysics.com/myct/assignment?assignmentID=1721971http://session.masteringphysics.com/myct/assignment?assignmentID=1721971


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AS!"#

:

)orrect

Part $

During t"e )arnot cycle, t"e oerall entropy 77777777

Hint $%& Some useful e'uations

Hint not displayed

AS!"#

:increases

decreases

remains constant

)orrect

Part C

3"ic" o+ t"e +ollo!ing gies t"e e++iciency o+ t"e )arnot engine6

Hint C%& Some useful e'uations

Hint not displayed

AS!"#

:


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)orrect

Part (

)onsider a )arnot engine operating bet!een t"e melting point o+ lead ( * and t"emelting point o+ ice ( * 3"at is t"e e++iciency o+ suc" an engine6

AS!"#

:0

0.

0.

1

in+inity

)orrect

Part "

3e "ae stressed t"at t"e )arnot engine does not e5ist in real li+e: -t is a purely t"eoreticaldeice, use+ul +or understanding t"e limitations o+ "eat engines 9eal engines neer operateon t"e )arnot cycle4 t"eir e++iciency is "ence lo!er t"an t"at o+ t"e )arnot engineo!eer, no attempts to build a )arnot engine are being made 3"y is t"at6

AS!"#

:# )arnot engine !ould generate too muc" t"ermal pollution

;uilding t"e )arnot engine is possible but is too e5pensie

T"e )arnot engine "as


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9ecall t"at in a )arnot cycle,

,

!"ere !e "ae taen all "eat e5c"anged to be positie ubstitute +or and in t"eearlier e5pression +or t"e e++iciency #lso recall t"at

>5press your ans!er in terms o+ , , and

AS!"#

: ?

)orrect

Heat "ngines Introduced

Learning Goal: To understand !"at a "eat engine is and its t"eoretical limitations

>er since ero demonstrated a crude steam turbine in ancient Greece, "umans "aedreamed o+ conerting "eat into !or -+ a +ire can boil a pot and mae t"e lid ump up anddo!n, !"y can't "eat be made to do use+ul !or6

# "eat engine is a deice designed to conert "eat into !or T"e "eat engines !e !ill study

!ill be cyclic: T"e !oring substance eentually returns to its original state sometime a+ter"aing absorbed a &uantity o+ "eat and done some !or # cyclic "eat engine cannot conert"eat into !or !it"out generating some !aste "eat in t"e process #lt"oug" by no meansintuitiely obious, t"is is an important +act o+ nature, since it dramatically a++ects t"etec"nology o+ energy generation -+ it were possible to conert "eat into !or !it"out any!aste "eat, t"en one !ould be able to build re+rigerators t"at are more t"an 100@ e++icient=

)onse&uently, t"e Aimpossible "eat engineA pictured sc"ematically "ere


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cannot e5ist, een in t"eory >ngineerstried "ard +or many years to mae suc" a deice, but adi )arnot proed in 182. t"at it !as

impossible

T"e ne5t +igure s"o!s an AidealA "eat

engine, one t"at obeys t"e la!s o+ t"ermodynamics -t taes in "eat at a temperature

and does !or -n t"e process o+ doing t"is it generates !aste "eat at a cooler

temperature

Tae and to be t"e magnitudes o+ t"e "eat absorbed and emitted, respectiely4 t"ere+ore bot" &uantities are positie

Part A

# "eat engine is designed to do !or T"is is possible only i+ certain relations"ips bet!eent"e "eats and temperatures at t"e input and output "old true 3"ic" o+ t"e +ollo!ing sets o+statements must apply +or t"e "eat engine to do !or6


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AS!"#

:and

and

and

and

)orrect

Part $

/ind t"e !or done by t"e AidealA "eat engine

>5press in terms o+ and

AS!"#

: ? )orrect

Part C

T"e thermal efficiency o+ a "eat engine is de+ined as +ollo!s:

>5press t"e e++iciency in terms o+ and

AS!"#

: ?

)orrect

Heat Pum,s and #efrigerators

Learning Goal: To understand t"at a "eat engine run bac!ard is a "eat pump t"at can beused as a re+rigerator

;y no! you s"ould be +amiliar !it" "eat enginesBBdeices, t"eoretical or actual, designed toconert "eat into !or Cou s"ould understand t"e +ollo!ing:

1 eat engines must be cyclical4 t"at is, t"ey must return to t"eir original state sometime a+ter "aing absorbed some "eat and done some !or*

2 eat engines cannot conert "eat into !or !it"out generating some !aste "eat int"e process

T"e second c"aracteristic is a rigorous result een +or a per+ect engine and +ollo!s +romt"ermodynamics # per+ect "eat engine is reersible, anot"er result o+ t"e la!s o+t"ermodynamics

-+ a "eat engine is run bac!ard (ie, !it" eery input and output reersed*, it becomes a


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heat pump (as pictured sc"ematically *

3or must be put into a "eat pump, and it t"en pumps "eat +rom a colder temperature

to a "otter temperature , t"at is, against t"e usual direction o+ "eat +lo! (!"ic" e5plains!"y it is called a A"eat pumpA*

T"e "eat coming out t"e "ot side o+ a "eat pump or t"e "eat going in to t"e cold side o+ a re+rigerator is more than t"e !or put in4 in +act it can be many times larger /or t"isreason, t"e ratio o+ t"e "eat to t"e !or in "eat pumps and re+rigerators is called t"e

coefficient of performance, -n a re+rigerator, t"is is t"e ratio o+ "eat remoed +rom t"e

cold side to !or put in:

-n a "eat pump t"e coe++icient o+ per+ormance is t"e ratio o+ "eat e5iting t"e "ot side tot"e !or put in:

Tae , and to be t"e magnitudes o+ t"e "eat emitted and absorbed respectiely

Part A

3"at is t"e relations"ip o+ to t"e !or done by t"e system6

Hint A%& ote the differences in wording

Hint not displayed


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>5press in terms o+ and ot"er &uantities gien in t"e introduction

AS!"# : ? )orrect

Part $

/ind , t"e "eat pumped out by t"e ideal "eat pump

Hint

$%&Conser*ation of energy and the first law

Hint not displayed

>5press in terms o+ and

AS!"#

: ? )orrect

Part C

# "eat pump is used to "eat a "ouse in !inter4 t"e inside radiators are at and t"e outside

"eat e5c"anger is at -+ it is a per+ect (ie, )arnot cycle* "eat pump, !"at is , itscoe++icient o+ per+ormance6

HintC%& Heat ,um, efficiency in terms of and

Hint not displayed

Hint

C%+ #elation -etween and in a Carnot cycle

Hint not displayed

Gie your ans!er in terms o+ and

AS!"#

: ?)orrect

Part (


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T"e "eat pump is designed to moe "eat T"is is only possible i+ certain relations"ips bet!een t"e "eats and temperatures at t"e "ot and cold sides "old true -ndicate t"estatement t"at must apply +or t"e "eat pump to !or

AS!"#

:and

and

and

and

)orrect

Part "

#ssume t"at you "eat your "ome !it" a "eat pump !"ose "eat e5c"anger is at ,

and !"ic" maintains t"e baseboard radiators at -+ it !ould cost 1000 to "eat t"e"ouse +or one !inter !it" ideal electric "eaters (!"ic" "ae a coe++icient o+ per+ormance o+1*, "o! muc" !ould it cost i+ t"e actual coe++icient o+ per+ormance o+ t"e "eat pump !ereE@ o+ t"at allo!ed by t"ermodynamics6

Hint

"%&.oney/ heat/ and the efficiency

T"e amount o+ money one "as to pay +or t"e "eat is directly proportional to t"e !or doneto generate t"e "eat T"us, t"e more e++icient t"e "eat generation t"e less !or needs to bedone and t"e lo!er t"e "eating bill

Cou are gien t"at t"e cost o+ is 1000 Cou also "ae an e&uation +or in terms o+t"e temperatures:

@

et t"is e&ual to and sole +or t"e monetary alue o+ , t"e amount o+ e5ternalenergy input t"e pump re&uires Cou can measure energies in units o+ currency +or t"is

calculationHint

"%+ 0nits of and

Hint not displayed

>5press t"e cost in dollars


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AS!"#

: )ost ?

18E)orrect

dollars

T"is saings is accompanied by more initial capital costs, bot" +or t"e "eat pump and +ort"e generous area o+ baseboard "eaters needed to trans+er enoug" "eat to t"e "ouse !it"out

raising , !"ic" !ould reduce t"e coe++icient o+ per+ormance #n additional problem isicing o+ t"e outside "eat e5c"anger, !"ic" is ery di++icult to aoid i+ t"e outside air is"umid and not muc" aboe


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#ccording to t"e second la! o+ t"ermodynamics, it is impossible +or 777777777777

AS!"#

:"eat energy to +lo! +rom a colder body to a "otter body

an ideal "eat engine to "ae t"e e++iciency o+ @

an ideal "eat engine to "ae nonB


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Part (

To increase t"e e++iciency o+ an ideal "eat engine, one must increase !"ic" o+ t"e+ollo!ing6

Hint (%& )ormula for the efficiency of an ideal engine

Hint not displayed

AS!"#

:t"e amount o+ "eat consumed per second

t"e temperature o+ t"e cold reseroir

t"e temperature o+ t"e "ot reseroir

t"e si


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/rom t"is e&uation, you can see t"at decreasing andHor increasing lead to an increase int"e e++iciency

Part )

3"y must eery "eat engine "ae a cold reseroir6

AS!"#

:;ecause it is impossible +or een a per+ect engine to conert "eatentirely into mec"anical !or

;ecause t"e cold reseroir eeps t"e engine +rom oer"eating

;ecause t"e cold reseroir eeps t"e engine +rom oercooling

;ecause t"e cold reseroir increases t"e po!er o+ t"e engine

)orrect

#not"er !ay to state t"e second la! o+ t"ermodynamics is as +ollo!s:

-t is impossible to construct a cyclical "eat engine !"ose sole e++ect is absorption o+ energy+rom t"e "ot reseroir and t"e per+ormance o+ t"e e&ual amount o+ !or

T"is statement is no!n as t"e elvin-!lanc" statement of the second law ote t"e !ordAsoleA

Cou "ae no! seen t"ree di++erent statements o+ t"e second la! Inderstanding t"ee&uialence o+ t"ese t"ree statements is important o!eer, it is not a triial matter: Courte5tboo and discussions s"ould "elp you to get a better grasp o+ t"is e&uialency

1 )rom Hot to Cool: The Second Law of Thermodynamics

Learning Goal: To understand t"e meaning and applications o+ t"e second la! o+

t"ermodynamics, to understand t"e meaning o+ entropy, and per+orm some basic calculationsinoling entropy c"angesT"e +irst la! o+ t"ermodynamics (!"ic" states t"at energy is consered* does not speci+y t"edirection in !"ic" t"ermodynamic processes in nature can spontaneously occur /ore5ample, imagine an obect initially at rest suddenly taing o++ along a roug" "ori


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T"e second law of thermodynamics dictates !"ic" processes in nature may occurspontaneously and !"ic" ones may not T"e second la! can be stated in many !ays, one o+!"ic" uses t"e concept o+ entropy

"ntro,y

>ntropy can be t"oug"t o+ as a measure of a system's disorder : # lo!er degree o+ disorderimplies lo!er entropy, and ice ersa /or e5ample, a "ig"ly ordered ice crystal "as arelatiely lo! entropy, !"ereas t"e same amount o+ !ater in a muc" less ordered state, suc"

as !ater apor, "as a muc" "ig"er entropy >ntropy is usually denoted by , and "as units o+

energy diided by temperature ( * /or an isothermal process (t"e temperature o+ t"esystem remains constant as it e5c"anges "eat !it" its surroundings*, t"e c"ange in a system'sentropy is gien by

,

!"ere is t"e amount o+ "eat inoled in t"e process and is t"e absolute temperature o+

t"e system T"e "eat is positie i+ t"ermal energy is absorbed by t"e system +rom itssurroundings, and is negatie i+ t"ermal energy is trans+erred +rom t"e system to itssurroundings

Ising t"e idea o+ entropy, t"e second la! can be stated as +ollo!s:

#he entropy of an isolated system may not decrease. $t either increases as the system

approaches equilibrium, or stays constant if the system is already in equilibrium.

#ny process t"at !ould tend to decrease t"e entropy o+ an isolated system could never occurspontaneously in nature /or a system t"at is not isolated, "o!eer, t"e entropy can increase,stay t"e same, or decrease

Part A

3"at "appens to t"e entropy o+ a bucet o+ !ater as it is cooled do!n (but not +ro


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most liely at a lo!er temperature t"an t"at o+ t"e bucet

Part $

3"at "appens to t"e entropy o+ a cube o+ ice as it is melted6

AS!"#

:

-t increases

-t decreases

-t stays t"e same

)orrect

Part C

3"at "appens to t"e entropy o+ a piece o+ !ood as it is burned6

AS!"#

:

-t increases

-t decreases

-t stays t"e same

)orrect

3"en a solid obect is turned into a gas, t"e degree o+ disorder increases, so t"e entropyincreases

Jet us try some calculations no!

Part (

#n obect at 20 absorbs 20 o+ "eat 3"at is t"e c"ange in entropy o+ t"e obect6>5press your ans!er numerically in oules per elin

AS!"#

: ?8KL102

)orrect

Part "

#n obect at 00 dissipates 20 o+ "eat into t"e surroundings 3"at is t"e c"ange in

entropy o+ t"e obect6 #ssume t"at t"e temperature o+ t"e obect does not c"angeappreciably in t"e process

>5press your ans!er numerically in oules per elinAS!"#

: ?B0)orrect

Part )

#n obect at .00 absorbs 20 o+ "eat +rom t"e surroundings 3"at is t"e c"ange in


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entropy o+ t"e obect6 #ssume t"at t"e temperature o+ t"e obect does not c"angeappreciably in t"e process>5press your ans!er numerically in oules per elin

AS!"#

: ?

N2

)orrect

Part G

T!o obects +orm a closed system Fne obect, !"ic" is at .00 , absorbs 20 o+ "eat

+rom t"e ot"er obect,!"ic" is at 00 3"at is t"e net c"ange in entropy o+ t"esystem6 #ssume t"at t"e temperatures o+ t"e obects do not c"ange appreciably in t"e process>5press your ans!er numerically in oules per elin

AS!"#

: ?12)orrect

ote t"at t"e net entropy c"ange is positive as t"e "eat is trans+erred +rom t"e "otter obectto t"e colder one -+ "eat !ere trans+erred in t"e ot"er direction, t"e c"ange in entropy!ould "ae been negative4 t"at is, t"e entropy o+ t"e system !ould "ae decreased T"isobseration, not surprisingly, is in +ull accord !it" t"e second la! o+ t"ermodynamics

1 PSS +2%& Heat "ngines

Learning Goal: To practice ProblemBoling trategy 201 eat >ngines

team at a temperature ? 280 and ? 100 enters a "eat engine at an unno!n

+lo! rate #+ter passing t"roug" t"e "eat engine, it is released at a temperature ? 100

and ? 100 T"e measured po!er output o+ t"e engine is N00 , and t"e e5iting

steam "as a "eat trans+er rate o+ ? K.0 /ind t"e e++iciency o+ t"e engine and t"e

molar +lo! rate o+ steam t"roug" t"e engine T"e constant pressure molar "eat capacity

+or steam is KE.E Pro-lem Sol*ing Strategy: Heat engines

-D>T-/C the relevant concepts: # "eat engine is any deice t"at conerts "eat partially to !or

>T IP the problem using the following steps:

1 )are+ully de+ine !"at t"e t"ermodynamic system is

2 /or multiBstep processes !it" more t"an one step, identi+y t"e initial and +inal states+or eac" step


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K -denti+y t"e no!n &uantities and t"e target ariables

. T"e +irst la!, , can be applied ust once to eac" step in a t"ermodynamic process, so you !ill o+ten need additional e&uations T"e e&uation

is use+ul in situations +or !"ic" t"e t"ermal e++iciency o+ t"e engine is releant -t's"elp+ul to setc" an energyB+lo! diagram

>O>)IT> the solution as follows:

1 ;e ery care+ul !it" t"e sign conentions +or and t"e arious 's is positie

!"en t"e system e5pands and does !or4 is negatie !"en t"e system is

compressed >ac" is positie i+ it represents "eat entering t"e system and isnegatie i+ it represents "eat leaing t"e system

2 Po!er is !or per unit time ( *, and "eat current is "eat trans+er per unit

time ( *

K eeping steps 1 and 2 in mind, sole +or t"e target ariables

>$#JI#T> your answer: Ise t"e +irst la! o+ t"ermodynamics to c"ec your results, paying particular attention toalgebraic signs

I("TI)3 the rele*ant conce,ts

T"is "eat engine partially conerts "eat +rom t"e incoming steam into !or, so t"e problemsoling strategy +or "eat engines is applicableS"T 0P the ,ro-lem using the following ste,s

Part A

3"ic" o+ t"e +ollo!ing &uantities are no!n6)"ec all t"at apply

AS!"#

:T"e po!er output o+ t"e engine,

T"e molar +lo! rate o+ steam,

T"e "eat trans+er rate +or steam leaing t"e engine,


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T"e temperature o+ steam as it leaes t"e engine,

T"e "eat trans+er rate +or steam entering t"e engine,

T"e temperature o+ t"e steam as it enters t"e engine,

T"e constant pressure molar "eat capacity o+ steam,T"e e++iciency o+ t"e engine,

)orrect

T"e e++iciency and t"e molar +lo! rate o+ steam t"roug" t"e engine are bot" target ariables

in t"is problem >en t"oug" t"e "eat trans+er rate o+ t"e steam entering t"e "eat engineis not gien in t"e problem statement, it is not a target ariable

T"e energyB+lo! diagram +or t"is system is s"o!n eat +lo!s into t"e engine at a rate o+

as steam at a temperature 3or leaes t"e engine at a rate T"e remaining "eat

leaes t"e engine at a rate o+ as steam at temperature

"4"C0T" the solution as follows

Part $

3"at is t"e e++iciency o+ t"e "eat engine6

Hint

$%&How to a,,roach the ,ro-lem

Cou are ased to +ind t"e e++iciency o+ t"e "eat engine

To +ind t"e e++iciency o+ t"e "eat engine, +irst +ind t"e "eat trans+er rate o+ t"e incomingsteam +rom t"e relations"ips bet!een !or and po!er and bet!een "eat and "eat trans+er


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rate Fnce you no! t"e incoming "eat trans+er rate, you can t"en calculate t"e e++iciencyo+ t"e "eat engine using t"e po!er deliered by t"e engine

Hint$%+

)ind the heat transfer rate of the incoming steam

3"at is t"e "eat trans+er rate o+ t"e incoming steam 6

Hint

$%+%&)ind an e5,ression for the heat transfer rate of the incoming steam

Hint not displayed

>5press your ans!er numerically in oules per second

AS!"# : ? .00)orrect

Hint

$%6)ind an e5,ression for the efficiency of the heat engine

Hint not displayed

>5press t"e e++iciency numerically to t"ree signi+icant +igures

AS!"#

: ?

01.8)orrect

#n e++iciency o+ 01.8 indicates t"at 1.8 o+ t"e "eat +rom t"e incoming steam is

conerted to !or T"e remaining 82 is e5pelled +rom t"e "eat engine as "eat in t"eoutlet steam

Part C

3"at is t"e molar +lo! rate o+ steam into t"e engine6

Hint

C%&How to a,,roach the ,ro-lem

Hint not displayed

Hint

C%+The net heat flowing into the heat engine

T"e "eat re&uired +or t"e temperature c"ange o+ moles o+ steam can be e5pressed interms o+ t"e di++erence in temperatures o+ t"e entering and e5citing steam as


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T"e "eat lost by t"e steam is e&ual to t"e "eat gained by t"e steam engine, so t"e net "eat

+lo!ing into t"e steam engine can be e5pressed as

Hint

C%6)ind an e5,ression for the molar flow rate of steam through the heat engine

>5press t"e molar +lo! rate o+ steam t"roug" t"e "eat engine as a +unction o+ t"e

generated po!er , t"e constant pressure molar "eat capacity , and t"e c"ange in

temperature eep in mind t"at is related to , and since t"e energy o+ t"e "eat

engine is consered,

>5press t"e molar +lo! rate in terms o+ , , and

AS!"#

: ? Answer not displayed

>5press t"e molar +lo! rate in moles per second to t"ree signi+icant +igures

AS!"#

: ?80L102

)orrect

no!ing t"e +lo! rate o+ steam t"roug" t"e "eat engine is important +or a +e! reasons -nt"e design stage, an estimate o+ t"e +lo! rate is used t"e si


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larger alue o+

)orrect

# "eat engine can produce more po!er eit"er by improing its e++iciency or by increasing

its t"roug"put -+ eit"er t"e entering "eat trans+er rate increases or t"e e5iting "eat trans+errate decreases, t"e po!er generated by t"e engine !ill increase Diiding bot" sides o+

by time maes t"e relations"ip bet!een po!er and "eat trans+er ratesclearer:

;y eit"er increasing t"e entering "eat trans+er rate or decreasing t"e e5iting "eat trans+errate, t"e e++iciency o+ t"e "eat engine is increased -+ t"e molar +lo! rate increases, t"eamount o+ "eat t"at t"e engine conerts into !or per unit time increases, but t"e engine is

not necessarily more e++icient

A Three8Ste, Gas Cycle

# monatomic ideal gas "as pressure and temperature -t is contained in a cylinder o+

olume !it" a moable piston, so t"at it can do !or on t"e outside !orld

)onsider t"e +ollo!ing t"reeBstep trans+ormation o+ t"e gas:

1 T"e gas is "eated at constant olume until t"e pressure reac"es (!"ere *

2 T"e gas is t"en e5panded at constant temperature until t"e pressure returns to

K T"e gas is t"en cooled at constant pressure until t"e olume "as returned to

-t may be "elp+ul to setc" t"is process on t"e p% plane

Part A

o! muc" "eat is added to t"e gas during step 1 o+ t"e process6Hint A%& )irst law of thermodynamics

T"e "eat added to a gas e&uals t"e c"ange in energy o+ t"e gas plus t"e !or done by t"e

gas:

Hint A%+ Thin9 a-out


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Hint not displayed

Hint A%6 How to find

T"e energy o+ a monatomic ideal gas is T"e number o+ gas particles

and t"e ;olt5press t"e !or done in terms o+ , , and

AS!"#

: ?)orrect

Part C


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o! muc" !or is done by t"e gas during step K6

-+ you'e dra!n a grap" o+ t"e process, you !on't need to calculate an integral to ans!ert"is &uestion

Hint

C%&The easy way to sol*e this ,ro-lem

Hint not displayed

Hint

C%+)ind the formula for wor9 done

Hint not displayed

>5press t"e !or done in terms o+ , , and

AS!"#

: ?)orrect

An Air Conditioner: #efrigerator or Heat Pum,?

T"e typical operation cycle o+ a common re+rigerator is s"o!n sc"ematically in t"e +igure

;ot" t"e condenser coils to t"e le+t andt"e eaporator coils to t"e rig"t contain a +luid (t"e !oring substance* called re+rigerant,!"ic" is typically in aporBli&uid p"ase e&uilibrium T"e compressor taes in lo!Bpressure,lo!Btemperature apor and compresses it adiabatically to "ig"Bpressure, "ig"Btemperatureapor, !"ic" t"en reac"es t"e condenser ere t"e re+rigerant is at a "ig"er temperature t"ant"at o+ t"e air surrounding t"e condenser coils and it releases "eat by undergoing a p"asec"ange T"e re+rigerant leaes t"e condenser coils as a "ig"Bpressure, "ig"Btemperature


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li&uid and e5pands adiabatically at a controlled rate in t"e e5pansion ale #s t"e +luide5pands, it cools do!n T"us, !"en it enters t"e eaporator coils, t"e re+rigerant is at a lo!er temperature t"an its surroundings and it absorbs "eat T"e air surrounding t"e eaporatorcools do!n and most o+ t"e re+rigerant in t"e eaporator coils apori5press your ans!er numerically in oules

AS!"#

: ?1L10

)orrect

Part $

-n eac" cycle, t"e c"ange in internal energy o+ t"e re+rigerant !"en it leaes t"e compresser

is 120L10 3"at is t"e !or done by t"e motor o+ t"e compressor6

Hint

$%&Adia-atic com,ression

Hint not displayed

>5press your ans!er in oules

AS!"#

: ?120L10

)orrect

Part C


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-+ t"e direction o+ t"e re+rigerant +lo! is inerted in an air conditioner, t"e air conditioningunit turns into a "eat pump and it can be used +or "eating rat"er t"an cooling -n t"is case,t"e coils !"ere t"e re+rigerant !ould condense in t"e air conditioner become t"e eaporator coils !"en t"e unit is operated as a "eat pump, and, ice ersa, t"e eaporator coils o+ t"eair conditioner become t"e condenser coils in t"e "eat pump uppose you operate t"e air

conditioner described in Parts # and ; as a "eat pump to "eat your bedroom -n eac" cycle,

!"at is t"e amount o+ "eat released into t"e room6 Cou may assume t"at t"e energyc"anges and !or done during t"e e5pansion process are negligible compared to t"ose +orot"er processes during t"e cycle

Hint

C%&How to a,,roach the ,ro-lem

Hint not displayed

Hint

C%+ )ind the right e5,resssion for the first law of thermodynamics

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>5press your ans!er numerically in oules

AS!"#

: ?NKL10

)orrect

Carnot Cycle#+ter )ount 9um+ord (;enamin T"ompson* and Qames Prescott Qoule "ad s"o!n t"ee&uialence o+ mec"anical energy and "eat, it !as natural t"at engineers belieed it possibleto mae a A"eat engineA (eg, a steam engine* t"at !ould conert "eat completely intomec"anical energy adi )arnot considered a "ypot"etical piston engine t"at containedmoles o+ an ideal gas, s"o!ing +irst t"at it !as reersible, and most importantly t"atR

regardless o+ t"e speci+ic "eat o+ t"e gasRit "ad limited e++iciency, de+ined as ,

!"ere is t"e net !or done by t"e engine and is t"e &uantity o+ "eat put into t"e engine

at a ("ig"* temperature /urt"ermore, "e s"o!ed t"at t"e engine must necessarily put an

amount o+ "eat bac into a "eat reseroir at a lo!er temperature

T"e cycle associated !it" a )arnot engine is no!n as a Carnot cycle # p% plot o+ t"e


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)arnot cycle is s"o!n in t"e +igure T"e

!oring gas +irst e5pands isot"ermally +rom state # to state ;, absorbing "eat +rom a

reseroir at temperature T"e gas t"en e5pands adiabatically until it reac"es a temperature

, in state ) T"e gas is compressed isot"ermally to state D, giing o++ "eat /inally, t"egas is adiabatically compressed to state #, its original state

Part A

3"ic" o+ t"e +ollo!ing statements are true6

Hint A%& Heat flow in an adia-atic ,rocess

Hint not displayed

)"ec all t"at apply

AS!"#

:/or t"e gas to do positie !or, t"e cycle must be traersed in acloc!ise manner

Positie "eat is added to t"e gas as it proceeds +rom state ) to state D

T"e net !or done by t"e gas is proportional to t"e area inside t"eclosed cureT"e "eat trans+erred as t"e gas proceeds +rom state ; to state ) isgreater t"an t"e "eat trans+erred as t"e gas proceeds +rom state D tostate #

)orrect

Part $

/ind t"e total !or done by t"e gas a+ter it completes a single )arnot cycle

Hint How to a,,roach the ,ro-lem


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$%&

Hint not displayed

Hint$%+

Com,ute the change in internal energy

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>5press t"e !or in terms o+ any or all o+ t"e &uantities , , , and

AS!"#

: ? )orrect

Part C

uppose t"ere are moles o+ t"e ideal gas, and t"e olumes o+ t"e gas in states # and ; are,

respectiely, and /ind , t"e "eat absorbed by t"e gas as it e5pands +rom state # tostate ;

Hint

C%& General method of finding

Hint not displayed

Hint

C%+ )ind the wor9 done -y the gas

Hint not displayed

Hint

C%6 #elation -etween and

Hint not displayed

>5press t"e "eat absorbed by t"e gas in terms o+ , , , t"e temperature o+ t"e "ot

reseroir, , and t"e gas constant

AS!"#

: ?

)orrect


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Part (

T"e olume o+ t"e gas in state ) is , and its olume in state D is /ind , t"emagnitude o+ t"e "eat t"at +lo!s out o+ t"e gas as it proceeds +rom state ) to state D

Hint

(%& How to a,,roach the ,ro-lem

Hint not displayed

>5press your ans!er in terms o+ , , , (t"e temperature o+ t"e cold reseroir*, and

AS!"#

: ?

)orrect

Fbsere t"at t"e t"ree parts toget"er imply t"at T"is is because ;) and

D# are adiabatic processes o using t"e +irst la!, ,

!"ereas o , or T"is is ageneral result: #ny t!o adiabatic processes operating bet!een t"e same t!o temperaturesresult in t"e same amount o+ !or, regardless o+ t"e pressure and olume di++erences

Part "

o!, by considering t"e adiabatic processes (+rom ; to ) and +rom D to #*, +ind t"e ratio

in terms o+ and

Hint"%&

How to a,,roach the ,ro-lem

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Hint

"%+ #ewrite in terms of and

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Hint

"%6 "5,ress and in terms of and

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Hint

"% "5,ress and in terms of and

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Hint "%;Sol*ing for in terms of and

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AS!"#

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)orrect

Part )

Ising your e5pressions +or and (+ound in Parts ) and D*, and your result +rom Part >,

+ind a simplified e5pression +or o olume ariables s"ould appear in your e5pression, nor s"ould any constants (eg, or

*

AS!"#

: ?

)orrect

Part G

T"e e++iciency o+ any engine is, by de+inition, )arnot proed t"at no engine can"ae an e++iciency greater t"an t"at o+ a )arnot engine /ind t"e e++iciency o+ a)arnot engine

Hint

G%& "5,ress the efficiency in terms of and

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>5press t"e e++iciency in terms o+ and AS!"#

: ?

)orrect

;ecause is generally +i5ed (eg, t"e cold reseroir +or po!er plants is o+ten a rier or alae*, engineers, trying to increase e++iciency, "ae al!ays soug"t to raise t"e upper


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temperature T"is e5plains !"y ("istorically* t"ere !ere some spectacular e5plosions o+ boilers used +or steam po!er

Carnot Heat "ngine Pressure *ersus 7olume Gra,h Conce,tual


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temperature T"is results in an increase in t"e gas's entropy o+

o!eer, "eat energy !ill naturally +lo! into t"e gas +rom t"e surroundings only i+ t"ere is a(slig"t* temperature di++erence bet!een t"e gas and t"e surroundings

Part $

-n a real isot"ermal e5pansion, t"e temperature o+ t"e surroundings must be77777777t"etemperature o+ t"e gas

Hint

$%&Heat flow and tem,erature difference

Hint not displayed

)omplete t"e sentence aboe

AS!"#

:greater t"an

less t"an

)orrect

Part C

;ecause o+ t"is temperature di++erence, t"e magnitude o+ t"e entropy lost by t"e

surroundings is 77777777 t"e magnitude o+ entropy gained by t"e gas during a realisot"ermal e5pansion

Hint

C%&.agnitude of the change in entro,y

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Hint

C%+Com,aring the entro,y changes

Hint not displayed


AS!"#

:greater t"an

e&ual to


32/51

less t"an

)orrect

Part (

;ecause o+ t"is di++erence in entropy c"ange, t"e net entropy c"ange o+ t"e entire system is 77777777 during a real isot"ermal e5pansion

Hint

(%&Total change in entro,y

Hint not displayed


AS!"#

:

positie

negatie


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;ecause o+ t"is temperature di++erence, t"e magnitude o+ t"e entropy gained by t"esurroundings is 7777777777 t"e magnitude o+ entropy lost by t"e gas during a realisot"ermal compression)omplete t"e sentence aboe

AS!"#

: greater t"ane&ual to

less t"an

)orrect

Part G

;ecause o+ t"is di++erence in entropy c"ange, t"e net entropy c"ange o+ t"e entire system is 77777777 during a real isot"ermal compression)omplete t"e sentence aboe

AS!"# :

positienegatie


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Hint A%6 "ntro,y change in an isothermal ,rocess

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>5press your ans!er numerically in oules per elin

AS!"#

: ?1E80)orrect

Part $

as t"e entropy o+ t"e aluminum bar decreased or increased6

Hint $%& How to a,,roach the 'uestion

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AS!"#

:ince t"e entropy c"ange o+ a system is al!ays positie, !e can deducet"at t"e entropy o+ t"e aluminum bar "as increasedince t"e +inal lo!er temperature o+ t"e bar means lo!er aerage speedo+ molecular motion, !e can deduce t"at t"e entropy o+ t"e bar "asdecreased3e don't "ae enoug" in+ormation to determine !"et"er t"e entropy o+t"e aluminum bar "as decreased or increased

)orrect

Part C

ince t"e aluminum bar is not an isolated system, t"e second la! o+ t"ermodynamicscannot be applied to t"e bar alone 9at"er, it s"ould be applied to t"e bar in combination!it" its surroundings (t"e lae*

#ssume t"at t"e entropy c"ange o+ t"e bar is BEK , !"at is t"e c"ange in total entropy

6

Hint

C%& Total change of entro,y

Hint not displayed



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AS!"#

: ?1E10)orrect

>en t"oug" t"e aluminum bar lo!ers its entropy, t"e total entropy c"ange o+ t"e bar andits surroundings (t"e !ater in t"e lae* is positie, and t"e total entropy increases

Part (

T"e second la! o+ t"ermodynamics states t"at spontaneous processes tend to beaccompanied by entropy increase )onsider, "o!eer, t"e +ollo!ing spontaneous processes:

• t"e gro!t" o+ plants +rom simple seeds to !ellBorgani


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+igure # gien amount o+ "eat is slo!lyadded to t"e gas, !"ile t"e piston allo!s t"e gas to e5pand in suc" a !ay t"at t"e gas's

temperature remains constant at

Part A

#s "eat is added, t"e pressure in t"is gas 7777777777

Hint A%& "5,ansion or contraction?

Hint not displayed

Hint A%+ Isothermal ,rocess

Hint not displayed

AS!"#

:increases

decreases

remains constant

cannot be determined

)orrect

Part $

-s t"e internal energy o+ t"e gas t"e same be+ore and a+ter is added6

Hint $%& )ind the formula for internal energy

Hint not displayed


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AS!"#

:

yes

no

)orrect

Part C

Does t"e second la! o+ t"ermodynamics +orbid conerting all o+ t"e absorbed "eat into!or done by t"e piston6

Hint C%& Second law of thermodynamics

Hint not displayed

AS!"#

:yes

no

)orrect

Part (

T"e (elinBPlanc statement o+ t"e* second la! o+ t"ermodynamics reads as +ollo!s:-t is impossible +or an engine !oring in a cycle to produce no ot"er e++ect t"an t"at o+e5tracting "eat +rom a reseroir and per+orming an e&uialent amount o+ !orT"e p"rase Ain a cycleA does not apply in t"is situation, so t"e second la! does not +orbid"eat being conerted entirely into !or /or t"is particular problem, is all o+ t"e "eatenergy absorbed by t"e gas in +act turned into !or done on t"e piston6

Hint (%& #elate / / and

Hint not displayed

AS!"# :

yes

no

)orrect

Part "


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Does t"e magnitude o+ t"e +orce t"at t"e gas e5erts on t"e piston depend on t"e piston'sarea6

Hint "%& )ind a formula for the force e5erted on the ,iston

Hint not displayed

AS!"#

:yes

no

)orrect

Part )

-s t"e total !or done by t"e gas independent o+ t"e area o+ t"e piston6

Hint )%& )ind a formula for the wor9 done on the ,iston

Hint not displayed

AS!"#

:yes

no

)orrect

Gien t"e same initial pressure o+ t"e gas, t"e greater t"e area o+ t"e piston, t"e larger t"e+orce on it o!eer, t"e !or done on t"e piston !"en "eat energy is added is

independent o+ piston area (because and * /rom t"is !e can in+er t"att"e +orce must act t"roug" a s"orter distance (ie, t"e piston does not moe as muc"* !"ent"e piston area is greater

Internal8Com-ustion "ngine Prototy,es #an9ing Tas9

i5 ne! prototypes +or internalBcombustion engines are tested in t"e laboratory /or eac"engine, t"e "eat energy input and output per cycle, and t"e designed number o+ cycles persecond are measured

Part A

9an t"ese engines on t"e basis o+ t"e !or t"ey per+orm per cycle

Hint A%& How to a,,roach the ,ro-lem

Hint not displayed


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AS!"#

:

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Irre*ersi-le *ersus #e*ersi-le Processes

Part A

3"ic" o+ t"e +ollo!ing conditions s"ould be met to mae a process per+ectly reersible6

Hint A%& #e*ersi-le ,rocesses

Hint not displayed

)"ec all t"at apply

AS!"#

:#ny mec"anical interactions taing place in t"e process s"ould be+rictionless#ny t"ermal interactions taing place in t"e process s"ould occuracross in+initesimal temperature or pressure gradients

T"e system s"ould not be close to e&uilibrium

)orrect

Part $

;ased on t"e results +ound in t"e preious part, !"ic" o+ t"e +ollo!ing processes are not reersible6

Hint

$%&How to a,,roach the ,ro-lem

Hint not displayed

)"ec all t"at apply

AS!"#

:Melting o+ ice in an insulated iceB!ater mi5ture at 0

Jo!ering a +rictionless piston in a cylinder by placing a bag o+ sand ontop o+ t"e pistonJi+ting t"e piston described in t"e preious statement by remoing onegrain o+ sand at a time

/ree


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#efrigerator Light

T"e inside o+ an ideal re+rigerator is at a temperature , !"ile t"e "eating coils on t"e bac

o+ t"e re+rigerator are at a temperature F!ing to a mal+unctioning s!itc", t"e lig"t bulb

!it"in t"e re+rigerator remains on !"en t"e t"e door is closed T"e po!er o+ t"e lig"t bulb is

4 assume t"at all o+ t"e energy generated by t"e lig"t bulb goes into "eating t"e inside o+t"e re+rigerator

/or all parts o+ t"is problem, you must assume t"at t"e re+rigerator operates as an ideal)arnot engine in reerse bet!een t"e respectie temperatures

Part A

-+ t"e temperatures inside and outside o+ t"e re+rigerator do not c"ange, "o! muc" e5tra

po!er does t"e re+rigerator consume as a result o+ t"e mal+unction o+ t"e s!itc"6

Hint A%& )ind the coefficient of ,erformance

/ind t"e re+rigerator's coe++icient o+ per+ormance

Hint

A%&%&#elate the heats e5changed to the wor9 done

T"e coe++icient o+ per+ormance is de+ined as , !"ere is t"e "eat absorbed

+rom t"e cold reseroir (t"e inside o+ t"e re+rigerator* and is t"e !or done by t"e

re+rigerator's motor -+ is t"e "eat gien o++ by t"e re+rigerator, +ind an e5pression +or


AS!"#

: ? )orrect

Hint

A%&%+#elating the heats and the wor9 to the a,,ro,riate tem,eratures

T"e absolute temperature scale may be de+ined by t"e +ollo!ing ratio:

,

!"ere and are t"e respectie "eats e5pelled to a cold reseroir and absorbed +rom a"ot reseroir +or an ideal )arnot engine 9ecall t"at !e are assuming t"e re+rigerator to be a )arnot engine operating in reverse, so t"at "eat is aborbed +rom t"e cold reseroirand e5pelled to t"e "ot reseroir T"at's !"at a good re+rigerator does, o+ course



42/51

AS!"#

: ?

)orrect

Hint A%+ How much heat is a-sor-ed from the cold reser*oir for the ,ro,erlywor9ing refrigerator?

uppose t"at, be+ore t"e lig"t !as on, t"e re+rigerator absorbed an amount o+ "eat +rom

t"e cold compartment during eery +i5ed time interal (3e could say, +or instance,

, but t"e +i5ed time interal !ill cancel in t"e +inal ans!er* #+ter t"e lig"t comeson, t"e temperature o+ t"e cold compartment s"ould not c"ange (according to t"e problem

statement* /or t"is to be true, "o! muc" "eat !ill t"e re+rigerator "ae to absorb in a

time !"ile t"e lig"t remains on6

>5press your ans!er in terms o+ , , and

AS!"# : ? Answer not displayed

Hint A%6 How much wor9 is done -y the malfunctioning refrigerator?

Hint not displayed

Hint A% Con*ert heat into ,ower

Hint not displayed

Hint A%; How much ,ower was consumed -y the ,ro,erly wor9ing refrigerator?

Hint not displayed

Hint A%= Putting it all together

Hint not displayed

>5press t"e e5tra po!er in terms o+ , , and

AS!"#

: ?

)orrect

Cou'll note t"at +or typical "ouse"old re+rigerators, t"is result suggests t"at +or a gien alue


43/51

o+ , t"e e5tra po!er needed to run t"e re+rigerator !it" t"e lig"t on is muc" smaller t"an

T"e ne5t part o+ t"is problem s"o!s t"is +or a speci+ic case

Part $

uppose t"e re+rigerator "as a 2B3 lig"t bulb, t"e temperature inside t"e re+rigerator is, and t"e temperature o+ t"e "eat dissipation coils on t"e bac o+ t"e re+rigerator is

/ind t"e e5tra po!er consumed by t"e re+rigerator eep in mind t"at you !ill need touse absolute units o+ temperature (ie, elins*>5press your ans!er numerically in !atts to t"ree signi+icant +igures

AS!"#

: ?K20)orrect

Si5 Carnot "ngines with 7arying #eser*oirs #an9ing Tas9

i5 )arnot engines operating bet!een di++erent "ot and cold reseroirs are described belo!T"e "eat energy trans+erred to t"e gas during t"e isot"ermal e5pansion p"ase o+ eac" cycle isindicated

Part A

9an t"ese engines on t"e basis o+ t"e c"ange in entropy o+ t"e gas during t"e isot"ermale5pansion p"ase o+ t"e cycle

Hint A%& Change in entro,y

T"e c"ange in entropy +or a reersible process t"at trans+ers "eat energy at

temperature is

9an +rom largest to smallest To ran items as e&uialent, oerlap t"em

AS!"#

:

$ie! )orrect

Part $

9an t"ese engines on t"e basis o+ t"e c"ange in entropy o+ t"e gas during one completecycle

Hint

$%&Change in entro,y for a com,lete cycle

http://openappletwindow%28%27850x500%27%2C%27assignmentproblemid%3D13843565%26partid%3D1%26expressionid%3D%26printview%3D1%26hidedetails%3D1%27%2C%27applet_id5254535%27%29/http://openappletwindow%28%27850x500%27%2C%27assignmentproblemid%3D13843565%26partid%3D1%26expressionid%3D%26printview%3D1%26hidedetails%3D1%27%2C%27applet_id5254535%27%29/


44/51

Hint not displayed

Hint

$%+

(oes the second law of thermodynamics a,,ly?

Hint not displayed

9an +rom largest to smallest To ran items as e&uialent, oerlap t"em

AS!"#

:

$ie! )orrect

Si5 ew Heat "ngines Conce,tual


45/51

AS!"#

:)/)orrect

Part $

3"ic" o+ t"e remaining designs iolate(s* t"e second la! o+ t"ermodynamics6Hint

$%&The second law of thermodynamics a,,lied to a heat engine

Hint not displayed

Gie t"e letter(s* o+ t"e design(s* in alp"abetical order, !it"out commas or spaces (eg,ABD*

AS!"#

:;D)orrect

Part C

3"ic" o+ t"e remaining designs "as t"e "ig"est t"ermal e++iciency6

AS!"#

:deice #

deice >

)orrect

1 )rom Hot to Cool: A Change in "ntro,y

-n a !ellBinsulated calorimeter, 10 o+ !ater at 20 is mi5ed !it" 10 o+ ice at 0

Part A

3"at is t"e net c"ange in entropy o+ t"e system +rom t"e time o+ mi5ing until t"e

moment t"e ice completely melts6 T"e "eat o+ +usion o+ ice is

ote t"at since t"e amount o+ ice is relatiely small, t"e temperature o+ t"e !ater remainsnearly constant t"roug"out t"e process ote also t"at t"e ice starts out at t"e melting point,and you are ased about t"e c"ange in entropy by t"e time it ust melts -n ot"er !ords, youcan assume t"at t"e temperature o+ t"e Aice !aterA remains constant as !ell


Hint not displayed

Hint A%+ (escri,tion of entro,y


46/51

Hint not displayed

Hint A%6 Heat needed to melt the ice

Hint not displayed

>5press your ans!er numerically in oules per elin Ise t!o signi+icant +igures in yourans!er

AS!"#

: ?8KL102

)orrect

#s you !ould e5pect, in t"is spontaneous process t"e net c"ange in entropy is positie: T"eentropy increases T"is is eident not ust +rom t"e calculation but also +rom t"e +act t"at acrystal becomes li&uid and "ence t"e degree o+ disorder increases

.elting Ice with a Carnot "ngine

# )arnot "eat engine uses a "ot reseroir consisting o+ a large amount o+ boiling !ater and acold reseroir consisting o+ a large tub o+ ice and !ater -n minutes o+ operation o+ t"e

engine, t"e "eat reected by t"e engine melts a mass o+ ice e&ual to N00L102

T"roug"out t"is problem use +or t"e "eat o+ +usion +or !ater

Part A

During t"is time, "o! muc" !or is per+ormed by t"e engine6


Hint not displayed

Hint A%+ Tem,erature con*ersion

Hint not displayed

Hint A%6 Calculate the heat re>ected

Hint not displayed


47/51

Hint A% Calculate the heat a-sor-ed

Hint not displayed

Hint A%; 0sing the first law of thermodynamics

Hint not displayed

AS!"#

: ?EK.0)orrect

#s you can see +rom t"is problem, it is ery important to eep in mind t"e signs o+ t"e "eatse5c"anged in an engine 3"en t"e )arnot engine absorbs "eat +rom a reseroir, t"e "eat!ill be a positie &uantity since t"e "eat is being added to t"e engine, be+ore it does any!or imilarly, !"en t"e )arnot engine reects "eat to a reseroir, t"e "eat !ill be anegatie &uantity since t"e "eat is lost +rom t"e engine T"e !or done by t"e engine, byt"e +irst la! o+ t"ermodynamics, is t"ere+ore t"e sum o+ all "eat c"anges in t"e engine

1 "ntro,y Change of an "5,anding Gas

T!o moles o+ an ideal gas undergo a reersible isot"ermal e5pansion +rom 2EL102 to

.8NL102 at a temperature o+ 21

Part A

3"at is t"e c"ange in entropy o+ t"e gas6Hint A%& How to a,,roach the ,ro-lem

Hint not displayed

Hint A%+ Calculate the wor9 done -y the gas

Hint not displayed

Hint A%6 Calculating the change in entro,y

Hint not displayed


AS!"#

: ? 10N


48/51


49/51

t"roug" a "eig"t o+ 10 6

AS!"#

:KE00)orrect

cycles

Pro-lem +2%;

# 1N0L102B cube o+ ice at an initial temperature o+ B180 is placed in 0E00 o+

!ater at .20 in an insulated container o+ negligible mass

Part A

)alculate t"e c"ange in entropy o+ t"e system

AS!"#

: ?K0)orrect

.ulti,le Choice ngine ;, in turn, reects "eat ata temperature o+ K20 T"e temperature at !"ic" engine # reects "eat to engine ;, in -units, is closest to:

AS!"#

:

K8

..

K

.E

.22

)orrect

.ulti,le Choice


50/51

# diesel engine operates reersibly on t"e cycle abcda, using 0 moles o+ an ideal gas

Pat"s bc and da are adiabatic processes T"e operating temperatures o+ points a, b, c, and d o+ t"e cycle are KE , .0 , .K2 , and 20 , respectiely T"e adiabatic constant o+ t"egas is 10

-n /ig 20., t"e "eat intae during t"e isobaric e5pansion, in Q, is closest to:

AS!"#

:2

2

KE

KK

.1

)orrect

Short Answer


51/51

AS!"#

:E080)orrect

Q

Part $

o! muc" "eat per cycle does t"is engine absorb at t"e "ot reseroir6

AS!"#

:1.L10.

)orrectQ

core ummary:Cour score on t"is assignment is 8@Cou receied 222N out o+ a possible total o+ 22 points

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