If the ratio of densities of two substances is $5: 6$ and the ratio of their specific heat capacities is $3: 5$, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is

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