To understand the quantitative relationships related to ideal (carnot) engines and the limitations of such devices imposed by the second law of thermodynamics.

in 1824, sadi carnot, a french engineer, introduced a theoretical engine that has been since then called a carnot engine, the most efficient engine possible. the following statement is known as carnot's theorem:

no engine operating between a hot and a cold reservoir can be more efficient than the carnot engine that operates between the same two reservoirs.

the carnot engine is a theoretical enginge with the maximum possible efficiency, somewhat like a "thought experiment." still, a carnot engine operates cyclically, just like any real engine. thecarnot cycle includes four reversible steps: two isothermal processes and two adiabatic ones.

in this problem, you will be asked several questions about carnot engines. we will use the following symbols:

qh: the absolute value (magnitude) of the heat absorbed from the hot reservoir during one cycle or during some time specified in the problem;
qc: the absolute value (magnitude) of the heat delivered to the cold reservoir during one cycle or during some time specified in the problem;
w: the amount of work done by the engine during one cycle or during some time specified in the problem;
th: the absolute temperature of the hot reservoir; and
tc: the absolute temperature of the cold reservoir.
part a

in general terms, the efficiency of a system can be thought of as the output per unit input. which of the expressions is a good mathematical representation of efficiency e of any heat engine?

in general terms, the efficiency of a system can be thought of as the output per unit input. which of the expressions is a good mathematical representation of efficiency of any heat engine?

e=qhw
e=qcqh
e=qcw
e=wqh
e=wqc
part b

during the carnot cycle, the overall entropy

during the carnot cycle, the overall entropy

increases
decreases
remains constant
part c

which of the following gives the efficiency of the carnot engine?

which of the following gives the efficiency of the carnot engine?

e=thtc
e=tcth
e=th? tcth
e=thtc+th
part d

consider a carnot engine operating between the melting point of lead (327? c) and the melting point of ice (0? c). what is the efficiency of such an engine?

consider a carnot engine operating between the melting point of lead () and the melting point of ice what is the efficiency of such an engine?

0
0.455
0.545
1
infinity
part e

we should stress again that the carnot engine does not exist in real life: it is a purely theoretical device, useful for understanding the limitations of heat engines. real engines never operate on the carnot cycle; their efficiency is hence lower than that of the carnot engine. however, no attempts to build a carnot engine are being made. why is that?

we should stress again that the carnot engine does not exist in real life: it is a purely theoretical device, useful for understanding the limitations of heat engines. real engines never operate on the carnot cycle; their efficiency is hence lower than that of the carnot engine. however, no attempts to build a carnot engine are being made. why is that?

a carnot engine would generate too much thermal pollution.
building the carnot engine is possible but is too expensive.
the carnot engine has zero power.
the carnot engine has too low an efficiency.
part f

a real heat engine operates between temperatures tc and th. during a certain time, an amount qc of heat is released to the cold reservoir. during that time, what is the maximum amount of work wmax that the engine might have performed?

express your answer in terms of qc, th, and tc.

wmax =