Practice question

**Heat engine** absorbs Q_h from hot reservoir T_h, does work W, rejects Q_c to cold T_c, efficiency η = W/Q_h =1 - Q_c/Q_h, second law limits η <1, Kelvin-Planck forbids perfect engine with Q_c=0, Clausius statement heat cannot flow spontaneously from cold to hot without work, equivalent to Kelvin-Planck. Δ Q = m s Δ T . m = 0.35 , s = 386.4 , Δ T = 45 - 15 = 30 . Δ Q = 0.35 × 386.4 × 30 = 4057.2 J ≈ 4057 J . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W =