$A$ 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 $R$?

$0.02 \, mol$ 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,$R = 8.31 \, J / K / mol$).

$A$ monatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals to $1$. What is the molar heat capacity of the gas?

An enclosed one mole of a monoatomic gas is taken through a process $A$ to $B$ as shown in the figure. The molar heat capacity of the gas for this process is

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$, if it is expanding under the condition $V \propto T^{2/3}$ is, $(R = 8.314 \ J/mol \cdot K)$ (in $J$)

$A$ gas is found to obey the law $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$,its final temperature becomes