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The Stirling cycle consists of two isothermal processes, at Th and Tc and two processes at constant volume, as shown in the attachment. The characteristics of the cycle depend on how the heat is transferred to and from the engine during the constant-volume parts of the cycle. Assume that the working substance is a perfect gas of point atoms so that U = cNRT, where c is a constant for the gas.
a) Consider first the case where only two heat reservoirs are available, at temperatures Th and Tc. Find the entropy change of the universe for section 41 of the cycle, and show that it is always positive.
(b) Justify the use of the word efficiency for the fraction (net work)/(Q12 +Q41)
for this cycle. Find the efficiency, so defined, for this cycle. Write your final answer in
terms of the Carnot efficiency ηC = 1 − Tc/Th.
(c) Now suppose that a continuous set of heat reservoirs, for every temperature
between Tc and Th, is available, so that 23 and 41 can be traversed reversibly. What
now is the efficiency of the cycle?
(d) In view of your answers to (b) and (c), explain the detrimental effect of the
increase in entropy in the former case.
