JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Heat & Thermodynamics

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A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

(A) $29 R T$
(B) $20 R T$
(C) $27 R T$ ✓ Correct
(D) $21 R T$

Answer: (C)

Solution

The internal energy of an ideal gas is

U = n C_{V} T

; for a mixture at a common temperature the individual internal energies simply add.

Argon is monatomic, so

C_{V, Ar} = \frac{3 R}{2}

. Oxygen is diatomic, and with vibrational modes neglected,

C_{V, O_{2}} = \frac{5 R}{2}

U = 8 \times \frac{3 R}{2} T + 6 \times \frac{5 R}{2} T = 12 R T + 15 R T = 27 R T

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Single correct option

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