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. W = P Δ V , P V = μ R T . Δ V = 11 - 5 = 6 L . P = (μ R T)/(V₁) = (1.4 × 8.3 × 370)/(5) = 860.44 atm (unit correction needed).Directly: W = μ R T ((V₂ - V₁)/(V₁)) , but W = P Δ V .