Thermodynamics

JEE Main level, single correct, medium

162 of 190

Question 162 of 190

A monoatomic gas is compressed from a volume of 2m32{m}^{3} to a volume of 1m31{m}^{3} at a constant pressure of 100Nm2100N{m}^{2}. Then it is heated at constant volume by supplying 150J150J of energy. As a result, the internal energy of the gas

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Answer: (B) Increases by 250J250J

Isobaric process with Q=0Q=0

∴0=W+ΔU∴0=\text{W}+\Delta \text{U}

∴0=PΔV+ΔU∴0=\text{P}\Delta \text{V}+\Delta \text{U}

∴ΔU=−PΔV∴\Delta \text{U}=-\text{P}\Delta \text{V}

=−100{1−2}J=-100\left\{1-2\right\}\text{J}

ΔU=100J\Delta \text{U}=100\text{J}

Constant volume with Q=150JQ=150J

Q=0+ΔU\text{Q}=0+\Delta \text{U}

∴ΔU2=150J∴\Delta {\text{U}}_{2}=150J

∴ΔU=ΔU1+ΔU2∴\Delta \text{U}=\Delta {\text{U}}_{1}+\Delta {\text{U}}_{2}

=+250J=+250J

Hence, internal energy increases by 250J250J

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