Two moles of a gas are expanded to double their volume by two different processes. One is isobaric and the other is isothermal. If $W_1$ and $W_2$ are the works done, respectively, then:

Consider two containers $A$ and $B$ containing identical gases at the same pressure,volume and temperature. The gas in container $A$ is compressed to half of its original volume isothermally while the gas in container $B$ is compressed to half of its original volume adiabatically. The ratio of final pressure of gas in $B$ to that of gas in $A$ is

$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is $\left(\gamma = \frac{5}{3}\right)$.

$A$ monoatomic gas at a pressure $P$,having a volume $V$ expands isothermally to a volume $4V$ and then adiabatically to volume $16V$. The final pressure of the gas is (Take $\gamma = \frac{5}{3}$)

In Column-$I$ devices and in Column-$II$ efficiency are given. Match them appropriately:

Column-$I$	Column-$II$
$(a)$ Heat engine	$(i)$ $\eta = \frac{Q_2}{Q_1 - Q_2}$
$(b)$ Heat pump	$(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$
	$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process,the internal energy $U$ obeys the equation $U = a V^3$,where $a$ is a constant. The work done during this process is