JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Chemical Thermodynamics

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The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

(A) $T_{1} = T_{2}$ ✓ Correct
(B) $T_{3} > T_{1}$
(C) $w_{isothermal} > w_{adiabatic}$ ✓ Correct
(D) $Δ U_{isothermal} > Δ U_{adiabatic}$ ✓ Correct

Answer: (A), (C), (D)

Solution

For an isothermal process, T₁ = T₂ (constant temperature), so (A) is correct. The isothermal curve lies above the adiabatic curve, so the work done (area under curve) is greater for isothermal expansion: wisothermal > wadiabatic, making (C) correct. For an isothermal process, ΔU = 0. For adiabatic expansion, the gas cools and ΔU < 0. Therefore ΔUisothermal > ΔUadiabatic, making (D) correct. Note: The official answer key states "ACD or AD" are both accepted.

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JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Chemical Thermodynamics

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