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 . 3 × 6¹.4 = 1 × V₂¹.4 . V₂¹.4 = 3 × 6¹.4 . V₂ = (3 × 6¹.4)¹/1.4 = 3¹/1.4 × 6 . 3⁰.714 ≈ 2.08 , 6¹.4 ≈ 12.29 , but directly: V₂ = 6 × 3¹/1.4 ≈ 12.48 L . Using first law ΔU = Q -