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Question

0.2 moles of an ideal gas at 360 K are compressed isothermally from 8 L to 2 L. What is the heat released? ( R = 8.3 J mol⁻¹ K⁻¹ )

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Explanation

**Isochoric process** constant volume ΔV=0, work W=0, first law ΔU = Q, all heat goes to internal energy, P/T = constant from ideal gas law P V = n R T at constant V, pressure proportional to temperature, P₁/T₁ = P₂/T₂, e.g., heating gas in rigid container pressure rises proportionally to T. Isothermal: Δ U = 0 , Δ Q = Δ W . W = μ R T ln((V₂)/(V₁)) . μ = 0.2 , T = 360 , V₂ = 2 , V₁ = 8 . W = 0.2 × 8.3 × 360 × ln((2)/(8)) = 597.6 × (-1.386) ≈ -829 J (work by

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