One kg of a diatomic gas is at a pressure of 8 × 10⁴ N/m². The density of the gas is 4 kg/m³. What is the energy of the gas due to its thermal motion? (a) 5 × 10⁴ J (b) 6 × 10⁴ J (c) 7 × 10⁴ J (d) 3 × 10⁴ J

Answer: (a). V = m/ρ = 1/4 = 0.25 m³ Diatomic: U = 5/2PV = 5/2 × 8 × 10⁴ × 0.25 U = 5 × 10⁴ J So the answer is (a) 5 × 10⁴ J.

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Q40JEE Main 2009 · AIEEEMedium

Degrees of Freedom & Internal Energy

One $\text{kg}$ of a diatomic gas is at a pressure of $8 \times 10^{4}\text{ N/m}^{2}.$ The density of the gas is $4\text{ kg/m}^{3}$ . What is the energy of the gas due to its thermal motion?

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Answer: (a)

$V = \frac{m}{\rho} = \frac{1}{4} = 0.25\ \text{m}^3$
Diatomic: $U = \frac{5}{2}PV = \frac{5}{2} \times 8 \times 10^4 \times 0.25$
$U = 5 \times 10^4$ J
So the answer is (a) $5 \times 10^4$ J.

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