Question

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^2}{4} R J / mol K$; then the value of $\alpha$ will be ____. (Assume that the given diatomic gas

Answer 1

$ C _{ v } / mix =\frac{ n _1 Cv _1+ n _2 Cv _2}{ n _1+ n _2}$
$ =\frac{1 \cdot \frac{3 R }{2}+3 \cdot \frac{5 R }{2}}{1+3} $
$ =\frac{9 R }{4}=\frac{\alpha^2}{4} R$
$ \alpha=3$