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Question

What is the change in internal energy for 0.5 moles of an ideal gas heated from 250 K to 300 K at constant volume? ( C_v = 20.8 J mol⁻¹ K⁻¹ )

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Explanation

**Cyclic process** system returns to initial state, ΔU=0 over cycle, net work W_net = area enclosed in P-V diagram, Q_net = W_net from first law ΔU= Q - W =0 => Q_net = W_net, clockwise cycle work done by system positive, counterclockwise work done on system negative, efficiency η = W_net/Q_in. Δ U = μ C_v Δ T . μ = 0.5 , C_v = 20.8 , Δ T = 300 - 250 = 50 . Δ U = 0.5 × 20.8 × 50 = 520 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P

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