An adiabatic vessel contains n 1 = 3 mole of diatomic gas. Moment of inertia of each molecule is I = 2.76 x 10 -46 kg m 2 and root-mean-square angular velocity is ω 0 = 5 × 1 0 1 2 rad/s . Another adiabatic vessel contains n 2 = 5 mole of a monatomic gas at a temperature 470 K. Assume gases to be ideal, calculate root-mean-square angular velocity of diatomic molecules when the two vessel are connected by a

Step-by-step solution

We know according to law of equipartition of energy, each gas molecule has 1/2 kT energy associated with each of its degrees of freedom. As a diatomic gas molecule has two rotational degrees of freedom, final temperature of the system is T f ⁡ = f ⁡ 1 n 1 T 1 + f ⁡ 2 n 2 T 2 f ⁡ 1 n 1 + f ⁡ 2 n 2 ...(i) Here for diatomic gas, f ⁡ 1 = 5 , n = 3 and T 1 = 250 K For monatomic gas, f ⁡ 2 = 3 , n 2 = 5 and T 2 = 470 K Thus from Eq. (i), T f ⁡ = 5 × 3 × 2 5 0 + 3 × 5 × 4 7 0 5 × 3 + 3 &times