In a process, the work done by the system is equal to the decrease in its internal energy. The process that the system undergoes is

N molecules each of mass $m$ of gas $A$ and 2 N molecules each of mass 2 m of gas $B$ are contained in a vessel which is maintained at a temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by $v_2^2$ and the mean square of the $x$-component velocity of the molecules of gas $A$ is denoted by $v_1^2$, then $v_1 / v_2$ is

The length of a metal rod at $30^{\circ} \mathrm{C}$ is 30 cm . If its temperature is raised to $105^{\circ} \mathrm{C}$, its length is increased by 0.027 cm . Then, the coefficient of linear expansion of the metal is

The heat energy required to convert 10 kg of ice at $-10^{\circ} \mathrm{C}$ into water at $0^{\circ} \mathrm{C}$ is (specific heat capacity of ice $=0.5 \mathrm{calg}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{calg}^{-1}$ )