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 $J$)

$1 \, \text{mole}$ of an ideal gas at temperature $T_1$ expands according to the law $P/V = \text{constant}$. Find the work done when the final temperature becomes $T_2$.

$A$ 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 $R$?

An ideal gas undergoes a quasi-static,reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = \text{constant}$,then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume,respectively):

Two thermodynamic processes are shown in the figure. The molar heat capacities for processes $A$ and $B$ are $C_A$ and $C_B$. The molar heat capacities at constant pressure and constant volume are represented by $C_P$ and $C_V$,respectively. Choose the correct statement.

In a process,temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$,where $K$ is a constant. In this process,the temperature of the gas is increased by $\Delta T$. The amount of heat absorbed by the gas is ($R$ is the gas constant).