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

An iron ball of mass $0.2\,kg$ is heated to $10\,^oC$ and put into a block of ice at $0\,^oC.$ $25\,g$ of ice melts. If the latent heat of fusion of ice is $80\,cal/g,$ then the specific heat of iron in $cal/g\,^oC$ is

A flask of volume $10^3\ cc$ is completely filled with mercury at $0\,^oC$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6}/^oC$ and that of glass is $40 \times 10^{-6}/^oC$. If the flask is now placed in boiling water at $100\,^oC$, …….. $cc$ mercury will overflow

On a new scale of temperature (which is linear) and called the $W$ scale, the freezing and boiling points of water are $39\,^oW$ and $239\,^oW$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39\,^oC$ on the Celsius scale ? …………. $^\circ \mathrm{W}$

The volume of a metal sphere increases by $0.15\%$ when its temperature is raised by $24\,^oC$.The coefficient of linear expansion of metal is