Question

One mole of monoatomic gas and one mole of diatomic gas are mixed together. What is the molar specific heat at constant volume for the mixture ?

• A. $\frac{3}{2} R$
• B. $2 R$
• C. $\frac{5}{2} R$
• D. $3 R$

Answer 1

Answer: (B)

For the mixture
$C_{v_{\text {mix }}} =\frac{\eta_{1} C_{v_{1}}+\eta_{2} C_{v_{2}}}{\eta_{1}+\eta_{2}}$
$\Rightarrow =\frac{\eta_{1}\left(\frac{R}{\gamma_{1}-1}\right)+\eta_{2}\left(\frac{R}{\gamma_{2}-1}\right)}{\eta_{1}+\eta_{2}}$
$\Rightarrow =\frac{R}{\eta_{1}+\eta_{2}}\left(\frac{\eta_{1}}{\gamma_{1}-1}+\frac{\eta_{2}}{\gamma_{2}-1}\right)$
Here, $\eta_{1} =1, \eta_{2}=1$
$\gamma_{1} =1.66, \gamma_{2}=1.4$
$C_{v_{\text{mix}}}=\frac{R}{1+1}\left[\frac{1}{1.66-1}+\frac{1}{1.4-1}\right]$
$\Rightarrow =\frac{R}{2}[4]$
$\Rightarrow =2 R$