The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6}/\,^oC$ and in a steel vessel is $144 \times 10^{-6}/\,^oC$. If $\alpha $ for steel is $12 \times 10^{-6}/\,^oC$, then $\alpha $ that of glass is

$P-V$ diagram of an ideal gas is as shown in figure. Work done by the gas in process $ABCD$ is

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$, while box $B$ contains one mole of helium at temperature $\left( {\frac{7}{3}} \right){T_0}$. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$ in terms of $T_0$ is

Figure below shows two paths that may be taken by a gas to go from a state $A$ to a state $C$. In process $AB$, $400\, J$ of heat is added to the system and in process $BC$, $100\, J$ of heat is added to the system. The heat absorbed by the system in the process $AC$ will be ............. $\mathrm{J}$

A monoatomic gas $(\gamma = 5/3)$ is suddenly compressed to $\frac{1}{8}$ of its original volume adiabatically, then the pressure of the gas will change to

$P-V$ diagram for two gases during adiabatic process are shown in the figure by curves $A$ and $B$ are for