A Carnot engine operates on 1 kg of methane, which we shall consider to be an ideal gas. Take γ = 1.35. The ratio of the maximum volume to the minimum volume is 4 and the cycle efficiency is 25 percent. Find the entropy increase of the methane during the isothermal expansion.
γ = cp/cv
η = .25 = 1-T1/T2
I know to consider the definition of ds (ds = dq/T), and apply it to the isothermal expansion.
Then consider how temperature and volume change for the adiabatic process and use the given information about the efficiency to get a relationship between the temperatures of the hot and cold reservoirs.
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Carnot cycle is explained on web page http://en.wikipedia.org/wiki/Carnot_cycle
We shall use the notations of Figure 2 on this web page.
The given ratio of the of the maximum volume to the minimum volume is
V_3/V_1 =4 (1)
in the notations of Figure 2. In the same notations we also can write
V_3/V_1 =V_3/V_2 ⋅V_2/V_1 ...
The solution discusses the entropy increase of the Carnot engine operating on methane.