Practice question

**Second law Kelvin-Planck statement** no process possible whose sole result is absorption of heat from reservoir and complete conversion to work, heat engine must have at least two reservoirs hot and cold, efficiency η = W/Q_h =1 - Q_c/Q_h <1, impossible 100% efficient, Carnot efficiency η_Carnot =1 - T_c/T_h maximum possible between T_h and T_c. P₁ V₁^γ = P₂ V₂^γ . 3 × 15^γ = 12 × 5^γ . (15^γ)/(5^γ) = (12)/(3) ⇒ ((15)/(5))^γ = 4 ⇒ 3^γ = 4 . γ = (log(4))/(log(3)) ≈ (0.602)/(0.477) ≈ 1.26 , but check PDF values: approximate γ = 1.33 . Using first law ΔU = Q -