Question

The specific heat of a monoatomic gas at constant pressure is $248.2\, J\, kg^{-1} K^{-1}$ and at constant volume it is $149.0\, J\, kg^{-1} K^{-1}$. Find the mean molar mass of the gas.

Answer 1

Molar heat capacity at constant pressure,
$C_{p} = 248.2 \times M J kg^{-1}$
where $M$ is the molar mass of the gas.
Similarly, $C_{v} = 149 \times M J kg^{-1}$
$C_{P} -C_{v} = R$
$\therefore 248.2 \times M -149M = 8.314$
$M= \frac{8.314}{248.2 -149} = 0.0838 kg/$mol
Molar mass of the gas $ = 83.8 g$/mol