Question

An ideal monatomic gas of mass $M$ is taken through a cyclic process $A B C$. The process $A B$ is $P \rho=$ constant. Total work done by the gas in the process is $-\frac{\alpha}{\beta} M \frac{P_{0}}{\rho_{0}}$. Find $(\alpha+\beta)$

Answer 1

$ W_{B \rightarrow C} =\rho_{0}\left(V_{f}-V_{i}\right) $
$=P_{0}\left(\frac{M}{\rho_{0}}-\frac{M}{3 \rho_{0}}\right)=\frac{2}{3} \frac{P_{0}}{\rho_{0}} M $
$W_{A \rightarrow C} =0 $
$ W_{\text {Total }} =\frac{-4}{3} \frac{P_{0}}{\rho_{0}} M+\frac{2}{3} \frac{P_{0}}{\rho_{0}} M$
$=\frac{-2}{3} \frac{P_{0}}{\rho_{0}} M $