The total internal energy of 2 moles of a monoatomic gas at a temperature $27^{\circ} \mathrm{C}$ is $U$. The total internal energy of 3 moles of a diatomic gas at a temperature $127^{\circ} \mathrm{C}$ is

A metal ball of mass 100 g at $20^{\circ} \mathrm{C}$ is dropped in 200 g of water at $80^{\circ} \mathrm{C}$. If the resultant temperature is $70^{\circ} \mathrm{C}$, then the ratio of specific heat of the metal to that of water is

Initially the pressure of 1 mole of an ideal gas is $10^5 \mathrm{Nm}^{-2}$ and its volume is 16 L . When it is adiabatically compressed, its final volume is 2 L . Work-done on the gas is