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10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P₁ to P₂ is α Joule (P₁ = 21.7 Pa and P₂ = 30 Pa, C_V = 21 J/K mol, R = 8.3 J/mol.K). The value of α is ______.

Asked in JEE Main 24th Jan 2nd Shift 2026 · Heat at constant volume and pressure

Figure: Heat at constant volume and pressure
Answer: (2) 21

Step-by-step solution

On the figure the step from P₁ to P₂ is vertical, at the fixed volume V=1 m³.

No volume change means no work, so all the heat goes into internal energy: Q=nC_VΔ T.

From PV=nRT at fixed V: Δ T=((P₂-P₁)V)/(nR)=((30-21.7)×1)/(10×8.3)=0.1 K.

Q=10×21×0.1.

α=21 J.

Why the other options are wrong

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