Question

A carnot engine uses 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 ${411}^{o}C$ and ${69}^{o}C$ respectively and the engine extract 1000 J of heat from the source in each cycle. Then,

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

Answer 1

Answer: (C)

the area enclosed by the P-V diagram in both cases is 500J.

Efficiency of a Carnot engine$\left(\eta \right)=1-\frac{T_c}{T_h}=\frac{W}{Q_h}$
Clearly, the efficiency of a Carnot engine doesn't depend upon the type of gas, i.e. whether its monatomic or diatomic.
$W=1000(1-\frac{342}{684})=1000(1-0.5)=500J$
Work done is 500J, i.e. the area enclosed in the PV diagram.
So, the work done in both cases is 500J.
Option C.