When the temperature of a gas in a closed vessel is increased by $2.4^{\circ} \mathrm{C}$, its pressure increases by $0.5 \%$. The initial temperature of the gas is

A gas is suddenly compressed such that its absolute temperature is doubled. If the ratio of the specific heat capacities of the gas is 1.5 , then the percentage decrease in the volume of the gas is

If the heat required to increase the rms speed of 4 moles of a diatomic gas from $v$ to $\sqrt{3} v$ is 83.1 kJ , then the initial temperature of the gas is

(universal gas constant $=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

The length of a metal rod is 20 cm and its area of cross-section is $4 \mathrm{~cm}^2$. If one end of the rod is kept at a temperature of $100^{\circ} \mathrm{C}$ and the other end is kept in ice at $0^{\circ} \mathrm{C}$, then the mass of the ice melted in 7 minutes is (Thermal conductivity of the metal $=90 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ and latent heat of fusion of ice $=336 \times 10^3 \mathrm{Jkg}^{-1}$ )