Kinetic Theory

JEE Main level, single correct, medium

164 of 168

Question 164 of 168

One kg of a diatomic gas is at a pressure of 8×104 N/m28 \times 10^4 \mathrm{~N} / \mathrm{m}^2. The density of the gas is 4 kg/m−34 \mathrm{~kg} / \mathrm{m}^{-3}. What is the energy of the gas due to its thermal motion?

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Answer: (B) 5×104 J5 \times 10^4 \mathrm{~J}

Thermal energy corresponds to internal energy
Mass =1 kg=1 \mathrm{~kg}
density =8 kg/m3=8 \mathrm{~kg} / \mathrm{m}^3
⇒\Rightarrow Volume = mass  density =18 m3=\frac{\text { mass }}{\text { density }}=\frac{1}{8} \mathrm{~m}^3
Pressure =8×104 N/m2=8 \times 10^4 \mathrm{~N} / \mathrm{m}^2
∴\therefore Internal Energy =52P×V=5×104 J=\frac{5}{2} \mathrm{P} \times \mathrm{V}=5 \times 10^4 \mathrm{~J}

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