An ideal gas sample ( γ = 1.5 ) is adiabatically compressed from a...

For an ideal gas, the molar heat capacity at constant volume $C_v$ is given by the relation:

$C_v = \dfrac{R}{\gamma - 1}$

Given that the adiabatic index $\gamma = 1.5$ and the universal gas constant $R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$, substituting these values yields:

$C_v = \dfrac{8.3}{1.5 - 1}$

$C_v = \dfrac{8.3}{0.5} = 16.6 \text{ J K}^{-1} \text{ mol}^{-1}$

The values of initial volume, final volume, pressure, and temperature are extraneous for this calculation.