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

Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} C$ is $W$. Then, the work done on heating $6$ moles of rigid diatomic gas through the same change in temperature is: (in $W$)

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:

One mole of an ideal gas at an initial temperature of $T \, K$ does $6 \, R \, \text{joules}$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$, the final temperature of the gas will be

$A$ sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given $\frac{C_{P}}{C_{V}}=\gamma=\frac{3}{2}$,$R=$ gas constant).

The heat capacity of one mole of an ideal gas is found to be $C_V = \frac{3R(1 + aRT)}{2}$,where $a$ is a constant. The equation obeyed by this gas during a reversible adiabatic expansion is