Determine the molar heat capacity for the thermodynamic process...

The equation of the process given in the figure is $p = \dfrac{K}{V^\gamma}$, which can be rewritten as $pV^\gamma = K$, where $K$ is a constant.

This is the standard equation for an adiabatic process of an ideal gas.

In an adiabatic process, there is no heat exchange between the system and its surroundings, which means $dQ = 0$.

The molar heat capacity is defined as $C = \dfrac{dQ}{n dT}$.

Since $dQ = 0$, the molar heat capacity for this process is $C = 0$.