The length of a metal bar is 20 cm and the ares of cross-section is $4 \times 10^{-4} \mathrm{~m}^2$. If one end of the rod is kept in ice at $0^{\circ} \mathrm{C}$ and the other end is kept in steamat $100^{\circ} \mathrm{C}$, the mass of ice melted in one minute is 5 g , the thermal conductivity of the matal in $\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ is (Latent heat of fusion $=80 \mathrm{cal} / \mathrm{g}$ )

The work done by an ideal gas of 2 moles in increasins its volume from $V$ to 2 V at constant temperature $T$ is V . The work done by an ideal gas of 4 moles in increasits its wolume from $V$ to $8 V$ at constant temperature $\frac{T}{2}$ is

When 403 of heat is absorbed by a monoatomic gas the increase in the internal energy of the gas is

In a Carnot engine, the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink. The efficiency of the engine is