$A$ gas obeys $P^2V = \text{constant}$. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume of $2V_0$,the final temperature is:

An ideal gas with heat capacity at constant volume $C_V$ undergoes a quasistatic process described by $p V^{\alpha} = \text{constant}$ in a $p-V$ diagram,where $\alpha$ is a constant. The heat capacity of the gas during this process is given by

$A$ diatomic gas follows the equation $PV^m =$ constant during a process. What should be the value of $m$ such that its molar heat capacity during the process is equal to $R$?

$A$ thermodynamic process for one mole of an ideal gas is shown below on a $P-V$ diagram. If $V_{2} = 2V_{1}$, then the ratio of temperature $T_{2} / T_{1}$ is ...... .

During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?

$0.02 \, mol$ of an ideal diatomic gas with initial temperature $20^{\circ} C$ is compressed from $1500 \, cm^3$ to $500 \, cm^3$. The thermodynamic process is such that $p V^2 = \beta$,where $\beta$ is a constant. Then,the value of $\beta$ is close to (the gas constant,$R = 8.31 \, J / K / mol$).