An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

A Carnot engine whose efficiency is $40 \%$, receives heat at 500 K . If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is

A system goes from $A$ and $B$ via two processes I and II as shown in figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes I and II respectively, then the relation between $\Delta U_1$ and $\Delta U_2$ is

A solid of 2 kg mass absorbs 50 kJ when its temperature is raised from $20^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$. The specific heat capacity of this solid in unit of $\mathrm{J} / \mathrm{kg}{ }^{\circ} \mathrm{C}$ is