The efficiency of a Carnot engine found to increase from $25 \%$ to $40 \%$ on increasing the temperature ( $T_1$ ) of source alone through 100 K . The temperature $\left(T_2\right)$ of the sink is given by

Match the following ( $f$ is number of degrees of freedom)

$$ \begin{array}{llll} \hline& \text { Gases } & & \frac{C_p}{C_v} \text { value } \\ \hline \text { A } & \text { Monoatomic } & \text { I } & \frac{4+f}{3+f} \\ \hline \text { B } & \text { Diatomic (rigid) } & \text { II } & \frac{5}{3} \\ \hline \text { C } & \text { Diatomic (non-rigid) } & \text { III } & \frac{7}{5} \\ \hline \text { D } & \text { Polyatomic } & \text { IV } & \frac{9}{7} \\ \hline \end{array} $$

A slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} \mathrm{C}$ and that of copper at $100^{\circ} \mathrm{C}$. If the thermal conductivities of brass and copper are in the ratio $1: 4$, then the temperature of interface is

A monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions, (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is