The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha _1$ and $\alpha _2$. If the difference between the two lengths is independent of temperatures

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha _1$ and $\alpha _2$ respectively. If the difference between the two length is independent of temperatures, then

Three perfect gases at absolute temperature $T_1 , T_2$ and $T_3$ are mixed. The masses of molecules are $m_1 , m_2$ and $m_3$ and the number of molecules are  $n_1 , n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha $, then coefficient of linear expansion of $B$

A metal rod of silver at $0°C$ is heated to $100°C$. It's length is increased by $0.19\, cm$. Coefficient of cubical expansion of the silver rod is