JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Heat & Thermodynamics

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A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be :

(A)8 RT
(B)16 RT
(C)4 RT
(D)11 RT✓ Correct

Answer: (D)

Solution

Oxygen (

O_{2}

) is diatomic with

C_{v} = \frac{5}{2} R

(3 translational + 2 rotational degrees of freedom). Neon is monatomic with

C_{v} = \frac{3}{2} R

(3 translational). The total internal energy is

U = n_{1} C_{v 1} T + n_{2} C_{v 2} T = 2 \times \frac{5}{2} R \times T + 4 \times \frac{3}{2} R \times T = 5 R T + 6 R T = 11 R T

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option

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