An ideal gas is found to obey $p V^{\frac{3}{2}}=$ constant during an adiabatic process. If such a gas initially at temperature $T$ is adiabatically compressed to $\frac{1}{4}$ th of its volume, then its final temperature is

The condition $d W=d Q$ holds good in the following process.

The efficiency of a Carnot engine found to increase from $25 \%$ to $40 \%$ on increasing the temperature ( $T_1$ ) of source alone through 100 K . The temperature $\left(T_2\right)$ of the sink is given by

Match the following ( $f$ is number of degrees of freedom)

$$ \begin{array}{llll} \hline& \text { Gases } & & \frac{C_p}{C_v} \text { value } \\ \hline \text { A } & \text { Monoatomic } & \text { I } & \frac{4+f}{3+f} \\ \hline \text { B } & \text { Diatomic (rigid) } & \text { II } & \frac{5}{3} \\ \hline \text { C } & \text { Diatomic (non-rigid) } & \text { III } & \frac{7}{5} \\ \hline \text { D } & \text { Polyatomic } & \text { IV } & \frac{9}{7} \\ \hline \end{array} $$