Internal energy of $\mathrm{n}_1$ moles of hydrogen at temperature ' $\mathrm{T}$ ' is equal to internal…

Internal energy of $\mathrm{n}_1$ moles of hydrogen at temperature ' $\mathrm{T}$ ' is equal to internal energy of ' $n_2$ ' moles of helium at temperature $2 T$, then the ratio $n_1: n_2$ is [Degree of freedom of $\mathrm{He}=3$, Degree of freedom of $\mathrm{H}_2=5$ ]
  1. 5:3
  2. 6:5
  3. 2:3
  4. 3:5

Solution

$\begin{aligned} & \mathrm{n}_1 \frac{5}{2} \mathrm{RT}=\mathrm{n}_2 \frac{3}{2} \mathrm{R}(2 \mathrm{~T}) \\ & \therefore \frac{\mathrm{n}_1}{\mathrm{n}_2}=\frac{6}{5}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 1)

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