A working substance goes through a cycle within which the absolute temperature varies `n-fold`, and the shape of the cycle is shown in
(a) Fig.a ,
(b) Fig. b, where `T` is the absolute temperature, and `S` the entropy. Find the efficiency of each cycle.

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Explanation

(a) we have from the definition
`Q = int TdS =` area under the curve
`Q_1 = T_0(S_1 - S_2)`
`Q'_2 = (1)/(2)(T_0 + T_1)(S_1 - S_0)`
Thus, using `T_1 = (T_0)/(n)`,
`eta = 1 - (T_0 + T_1)/(2 T_0) = 1 -(1 + (1)/(n))/(2) = (n -1)/(2n)`
(b) Here `Q_1 = (1)/(2) (S_1 - S_0)(T_1 + T_2)`
`Q'_2 = T_1 (S_1 - S_0)`
`eta = 1 -(2 T_1)/(T_1 + T_2) = (T_0 - T_1)/(T_0 -T_1) = (n -1)/(n + 1)`.
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