The initial pressure and volume of a gas are $P$ and $V$ respectively. First, it is expanded isothermally to a volume $4V$ and then compressed adiabatically to a volume $V$. The final pressure of the gas will be (given $\gamma = 3/2$): (in $P$)

An ideal gas with pressure $P$,volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. The same gas is expanded adiabatically to a volume $2V$,the final pressure is $P_a$. In terms of the ratio of the two specific heats for the gas $\gamma$,the ratio $\frac{P_i}{P_a}$ is

Five moles of an ideal gas has pressure $p_0$,volume $V_0$,and temperature $T_0$. The gas is expanded to volume $3V_0$ along a path such that the pressure $p$ changes as a function of volume $V$ as $p = p_0(V/V_0)$. The pressure is then reduced to $p_0$ while maintaining constant volume. Finally,the gas undergoes an isobaric compression until the volume and temperature return to $V_0$ and $T_0$,respectively. The total work done by the gas during the entire process is:

The relation between the efficiency $\eta$ of a heat engine and the coefficient of performance $\alpha$ of a refrigerator is:

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. The $P-T$ diagram that represents the same process is

The internal energy of the air in a room of volume $V$ at temperature $T$,with outside pressure $P$ increasing linearly with time,varies as