$A$ mixture of gases at $STP$ for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{9}$th of its original volume. The final temperature of the mixture is .......... $^{\circ}C$.

$A$ diatomic gas undergoes an adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^{x}$, where $x$ is:

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

In which of the following processes,heat is neither absorbed nor released by a system?

One mole of an ideal gas $(C_p/C_v = \gamma)$ at absolute temperature $T_1$ is adiabatically compressed from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by

$5.6 \text{ liter}$ of helium gas at $STP$ is adiabatically compressed to $0.7 \text{ liter}$. Taking the initial temperature to be $T_1$,the work done in the process is