Question

Assuming $R=8.3J{mol}^{-1}{K}^{-1}$ and $\gamma =1.4$ the values of $C_p$ and $C_v$ of a gas are:

• A. $29.05J{mol}^{-1}{K}^{-1},20.75J{mol}^{-1}{K}^{-1}$
• B. $20.75J{mol}^{-1}{K}^{-1},29.05J{mol}^{-1}{K}^{-1}$
• C. $16.60J{mol}^{-1}{K}^{-1},8.300J{mol}^{-1}{K}^{-1}$
• D. $8.300J{mol}^{-1}{K}^{-1},16.60J{mol}^{-1}{K}^{-1}$

Answer 1

Answer: (A)

$29.05J{mol}^{-1}{K}^{-1},20.75J{mol}^{-1}{K}^{-1}$

$\gamma =\frac{C_p}{C_v}=1.4\Rightarrow C_p=1.4C_v$

$R=C_p-C_v=8.3$

$\Rightarrow 1.4C_v-C_v=8.3\Rightarrow 0.4C_v=8.3$

$\Rightarrow C_v=\frac{8.3}{0.4}=\frac{83}{4}=20.75J{mol}^{-1}{K}^{-1}$

$\Rightarrow C_p=C_v+R$
$=20.75+8.3=29.05J{mol}^{-1}{K}^{-1}$