The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be ______ $\times 10^{6} \mathrm{~J}$. (Consider air as diatomic molecule)

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Heat & Thermodynamics

The internal energy of air in

4 m \times 4 m \times 3 m

sized room at 1 atmospheric pressure will be ______

\times 1 0^{6} J

.
(Consider air as diatomic molecule)

Answer: 12

Solution

For an ideal gas, internal energy is:

U = n C_{v} T

For a diatomic gas:

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

Using the ideal gas equation PV = nRT:

U = n \times \frac{5 R}{2} \times T = \frac{5}{2} n R T = \frac{5}{2} P V

Given:

P = 1 atm = 10⁵ Pa
V = 4 × 4 × 3 = 48 m³

U = \frac{5}{2} \times 1 0^{5} \times 48 = \frac{5 \times 48}{2} \times 1 0^{5} = 120 \times 1 0^{5} = 12 \times 1 0^{6}

J

Therefore, the internal energy is 12 × 10⁶ J.

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Integer answer

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