A diatomic gas is heated in a vessel to a temperature of 10000K. … - Vidyadip

Question

A diatomic gas is heated in a vessel to a temperature of 10000K. If each molecule possess an average energy $E_1$. After sometime, a few molecule escape into the atmosphere at 300 K. Due to which, their energy changes to $E_2$. Calculate the ratio of $\frac{\text{E}_1}{\text{E}_2}.$

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Answer

Number of degrees of freedom of diatomic gas at 10000K = 7 Number of degrees of freedom of diatomic gas at 300K = 5$\therefore\frac{\text{E}_1}{\text{E}_2}=\frac{\big(\frac{7}{2}\big)\text{k}_{\text{B}}\text{T}_1}{\big(\frac{5}{2}\big)\text{k}_{\text{B}}\text{T}_2}$
$=\frac{7}{5}\times\frac{\text{T}_1}{\text{T}_1}=\frac{7}5{}\times\frac{10000}{300}=\frac{140}{3}$

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