One gram of a liquid is converted to vapour at $3 \times 10^5 \text{ Pa}$ pressure. If $10\%$ of the heat supplied is used for increasing the volume by $1600 \text{ cm}^3$ during this phase change, then the increase in internal energy in the process will be

Match the devices in Column-$I$ with their efficiency/coefficient of performance in Column-$II$:

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

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ graph?

$A$ monoatomic gas of 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 (ratio of specific heats $\gamma = \frac{5}{3}$)

Write the equation for the work done during the compression of an ideal gas.

$A$ sample of an ideal gas is taken through the cyclic process $ABCA$ as shown in the figure. It absorbs $40 \ J$ of heat during the part $AB$,no heat during $BC$,and rejects $60 \ J$ of heat during $CA$. $A$ work of $50 \ J$ is done on the gas during the part $BC$. The internal energy of the gas at $A$ is $1560 \ J$. The work done by the gas during the part $CA$ is.............$J$.