$50\, gm$ of copper is heated to increase its temperature by $10\,^oC$. If the same quantity of heat is given to $10\, gm$ of water, the rise in its temperature is ........ $^oC$ (Specific heat of copper $=420\, Joule\, kg^{-1}\,^oC^{-1}$)

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

On heating a liquid of coefficient of cubical expansion $\gamma $ in a container having coefficient of linear expansion $\gamma /3,$ the level of liquid in the container will

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 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 vessel $A$ is $\alpha $, the coefficient of linear expansion of vessel $B$ is

Two holes of unequal diameters $d_1$ and $d_2\, (d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated