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. P₁ V₁^γ = P₂ V₂^γ . 6 × 12¹.5 = 2 × V₂¹.5 . V₂¹.5 = (6)/(2) × 12¹.5 = 3 × 12¹.5 . 12¹.5 = 12 × 12⁰.5 ≈ 41.57 , V₂¹.5 = 3 × 41.57 ≈ 124.71 . V₂ = (124.71)¹/1.5 = (124.71)²/3 ≈ 25 L . Using first law ΔU = Q -