For a certain process, the pressure of a diatomic gas varies according to the relation $P = aV^2$, where $a$ is a constant. What is the molar heat capacity of the gas for this process?

The variation of pressure $P$ with volume $V$ for an ideal diatomic gas is parabolic as shown in the figure. The molar specific heat of the gas during this process is

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.

One mole of a monoatomic ideal gas is expanded by a process described by $p V^3 = C$,where $C$ is a constant. The heat capacity of the gas during the process is given by ($R$ is the gas constant).

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

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