The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_P$ and $C_V$ respec

Question

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_P$ and $C_V$ respectively. If $\gamma = C_P/C_V$ and $R$ is the universal gas constant, then $C_V$ is equal to:

Accepted Answer

For an ideal gas, the relationship between the molar heat capacity at constant pressure ($C_P$) and at constant volume ($C_V$) is given by Mayer's relation: $C_P - C_V = R$ . 
Given the ratio of specific heats is $\gamma = \frac{C_P}{C_V}$, we can substitute $C_P = \gamma C_V$ into Mayer's relation:
$\gamma C_V - C_V = R$
$C_V(\gamma - 1) = R$
$C_V = \frac{R}{\gamma - 1}$.

Step-by-Step Solution

Practice All PHYSICS Questions