$A$ 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 $R$?

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P = kV$ ($k$ is a constant). If the final temperature is $2T_0$,the heat supplied to the gas is:

Find the amount of work done to increase the temperature of one mole of an ideal gas by $30^o\ C$ if it is expanding under the condition $V \propto T^{2/3}$. $[R = 1.99 \ cal/mol-K]$

One mole of an ideal monoatomic gas at temperature $T_0$ expands slowly according to the law $P/V = \text{constant}$. If the final temperature is $2 T_0$, heat supplied to the gas is:

Suppose an ideal gas follows the process $VP^3 = \text{constant}$. The initial temperature and volume of the gas are $T$ and $V$ respectively. If the gas expands to $27V$, then its final temperature will be:

In a thermodynamic process, $2 \, \text{moles}$ of a monatomic ideal gas obey $P \propto V^{-2}$. If the temperature of the gas increases from $300 \, K$ to $400 \, K$, find the work done by the gas in terms of $R$ (where $R$ is the universal gas constant).