A Carnot engine used first an ideal monoatomic gas `(gamma = 5//3)` and then an ideal diatomic gas `(gamma = 7//5)` as its working substance. The source and sink temperatures are `411^(@)C` and `69^(@)C` respectively and the engine extracts `1000 J` of heat from the source in each cycle. then

Options

A. the efficient of the engine in the two cases are in the ratio `21 : 25`
B. the area enclosed by the P-V diagram in the first case only is `500 J`
C. the area enclosed by the P-V diagram in both cases only is `500 J`
D. the heat energy rejected by the engine in the first case is `600 J` while that in the second case is `714.3 J`

Answer

C

Explanation

`eta=1-(T_L)/(T_H) = 1-(342)/(684)= 1/2`
Now `eta = W/Q` or `1/2 = w/(100) or W = 500J`.