A rectangular ice box of total surface area of $1000 \mathrm{~cm}^2$ initially contains 1.5 kg of ice at $0^{\circ} \mathrm{C}$. If the thickness of the walls of the box is 2 mm and the temperature outside the box is $42^{\circ} \mathrm{C}$, then the mass of the ice remaining in the box after 160 minutes is

(Thermal conductivity of the material of the box $=10^{-2} \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and latent heat of the fusion of ice $=336 \times 10^3 \mathrm{Jkg}^{-1}$ )

At constant pressure, equal amounts of heat are supplied to a monoatomic gas and a diatomic gas separately. The ratio of the increases in internal energies of the two gases is

If the rms speed of the molecules of a gas at a temperature of $77^{\circ} \mathrm{C}$ is $50 \mathrm{~ms}^{-1}$, then the rms speed of the same gas molecules at a temperature of $150.5^{\circ} \mathrm{C}$ is

To increase the length of a metal rod by $0.4 \%$ the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $\left.=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)$