An ideal rigid diatomic gas $(\gamma = 7/5)$ undergoes an adiabatic change. If the relation between temperature and volume is $TV^x = \text{constant}$, then the value of $x$ is:

The relation obeyed by a perfect gas during an adiabatic process is $PV^{3/2} = \text{constant}$. The initial temperature of the gas is $T$. When the gas is compressed to half of its initial volume, the final temperature of the gas is:

An ideal gas undergoes an adiabatic process from state $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. The work done during the process is ..... (where $\mu$ = number of moles,$C_P$ and $C_V$ = molar specific heats).

The $P-V$ diagram of a diatomic ideal gas system undergoing a cyclic process is shown in the figure. The work done during the adiabatic process $CD$ is (use $\gamma=1.4$) (in $J$):

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, \rho)$ to $(P^{\prime}, \rho^{\prime})$. If $\frac{\rho^{\prime}}{\rho}=32$,then $\frac{P^{\prime}}{P}$ is:

When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor of $2$. The value of the adiabatic constant $\gamma$ is