Question

Define molar specific heat of a gas at constant volume (CV) and constant pressure (Cp). Obtain the
ratio Cp/Cv for a hydrogen gas using the law of equipartition of energy.

Answer 1

Answer on Question #53683, Physics Mechanics Kinematics Dynamics

Define molar specific heat of a gas at constant volume $(C_{\mathrm{V}})$ and constant pressure $(C_{\mathrm{p}})$. Obtain the ratio $C_{\mathrm{p}} / C_{\mathrm{V}}$ for a hydrogen gas using the law of equipartition of energy.

Solution

If $\Delta V = \text{const}$ then $Q = \Delta U = \frac{i}{2} n R \Delta T$ (where $n$ number of moles; $R = 8.314 J / (K \cdot \text{mol})$ is the gas constant; $i$ is the number of degrees of freedom), and $C_V = \frac{Q}{\nu \Delta T} = \frac{i}{2} R$.

If $\Delta p = \text{const}$ then $Q = \Delta U + A = \frac{i}{2} n R \Delta T + n R \Delta T = \frac{i + 2}{2} n R \Delta T$ and $C_p = \frac{Q}{\nu \Delta T} = \frac{i + 2}{2} R$.

For a diatomic gas (such as hydrogen), the number of degrees of freedom $i = 5$.

So, $C_p / C_V = \frac{i + 2}{i} = \frac{5 + 2}{5} = 7 / 5$.

**Answer**: $C_p / C_V = \frac{i + 2}{i} = 7 / 5$

http://www.AssignmentExpert.com/