The graph of pressure $(P)$ and volume $(V)$ according to $PV^n = C$,where $n = 1.4$. Identify the correct graph.

The figure shows a process $AB$ undergone by $2$ moles of an ideal diatomic gas. The process $AB$ follows the relation $VT = \text{constant}$. Given $T_1 = 300 \text{ K}$ and $T_2 = 500 \text{ K}$ ($R$ is the gas constant).

An ideal gas expands in such a way that $PV^2 =$ constant throughout the process.

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 $V$. When the gas expands to a volume $2V$,its temperature will be:

$Q$ amount of heat is given to $0.5 \text{ mole}$ of an ideal mono-atomic gas by a process $TV^n = \text{constant}$. The following graph shows the variation of temperature with $Q$. Find the value of $n$.

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