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Question

A monatomic gas undergoes an adiabatic expansion from 740 K to 370 K with 0.7 moles . What is the work done? ( R = 8.3 J mol⁻¹ K⁻¹ , gamma = 1.67 )

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Explanation

**Isobaric process** constant pressure, work W = P ΔV = P(V₂ - V₁) = n R ΔT, for expansion ΔV positive W positive, for compression negative, heat Q = n C_p ΔT, ΔU = n C_v ΔT. Isothermal process constant temperature ΔU=0, work W = n R T ln(V₂/V₁) = n R T ln(P₁/P₂), Q = W, heat absorbed equals work done. W = (μ R (T₁ - T₂))/(γ - 1) . μ = 0.7 , R = 8.3 , T₁ = 740 , T₂ = 370 , γ = 1.67 . W = (0.7 × 8.3 × (740 - 370))/(1.67 - 1) = (5.81

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