Question

One mole of a non-linear triatomic gas is heated in a closed rigid container from ${500}^{\circ }C$ to ${1500}^{\circ }C$. The amount of energy required is $500xR$ if the vibrational degree of freedom become effective only above ${1000}^{\circ }C$. Find the value of $x$.

Answer 1

$Q=C_{V_1}(1000-500)+C_{V_2}(1500-1000)$

$Q=(\frac{3R}{2}+\frac{3R}{2})\times 500+(\frac{3R}{2}+\frac{3R}{2}+3R)\left(500\right)$

$Q=1500R+3000R=4500R$

Therefore, value of $x=9$.