One mole of mono atomic gas is mixed with three moles of diatomic gas. What is molecular specific heat of the mixture at constant volume?R=8.31 J/mole/K

for mono atomic gas  specific heat of gas at constant volume is ${\text{C}}_{\text{v}}=3R/2$

For diatomic gas ${\text{C}}_{\text{v}}=5R/2$

${\left({\text{C}}_{\text{v}}\right)}_{\text{mix}}\text{=}\frac{{\text{n}}_1{\text{C}}_{{\text{v}}_1}{\text{+n}}_2{\text{C}}_{{\text{v}}_2}}{{\text{(n}}_1{\text{+n}}_2\text{)}}\text{=}\frac{\text{1×}\frac{\text{3}}{\text{2}}\text{R+3×}\frac{\text{5}}{\text{2}}\text{R}}{\text{1+3}}=\frac{9}{4}\text{R}=\frac{9}{4}\times 8.31=18.7 J/mole/K.$