Question

Why is ${\mathbf{C}}_{\mathbf{p}}$larger than ${\mathbf{C}}_{\mathbf{V}}$ ? Provide a conceptual rationale.

Short answer

${\mathrm{C}}_{\mathrm{P}}$is greaterthan${\mathrm{C}}_{\mathrm{V}}$because in${\mathrm{C}}_{\mathrm{P}}$some heat is absorbed for increasing the internal energy as well as for doing the work whereas in${\mathrm{C}}_{\mathrm{V}}$it is usedonly for raising internal energy.

Step-by-step solution

About CP  and  CV.

The ${\mathrm{C}}_{\mathrm{P}}$ is a term used to represent the molar heat capacity of a substance at constant pressure.

The ${\mathrm{C}}_{\mathrm{V}}$ is a term used to represent the molar heat capacity of a substance at constant volume.

Also, the ratio of these particular heat capacities is given by ${\text{C}}_{\text{p}}{\text{/C}}_{\text{v}}$.

 

When pressure is constant, some heat is absorbed for increasing the internal energy as well as for doing the work.

$\mathbf{W}\mathbf{=}\mathbf{P\Delta V}$

Whereas for constant volume, heat is absorbed only for raising internal energy, not work, since the change in volume is zero.

$\mathbf{W}\mathbf{=}\mathbf{P\Delta V}$for closed system. Here, $\mathbf{\Delta V}\mathbf{=}\mathbf{0}$

Hence, more heat is required in case of ${\mathrm{C}}_{\mathrm{P}}$ as compared to ${\mathrm{C}}_{\mathrm{V}}$.