Practice question

**Carnot engine** reversible engine operating between T_h and T_c has maximum efficiency η =1 - T_c/T_h, T in kelvin, e.g., T_h=400 K T_c=300 K η=0.25, real engines less due to irreversibilities, second law defines direction of spontaneous processes and entropy increase. For adiabatic: P₁ V₁^γ = P₂ V₂^γ . 9 × 30^γ = 1 × 90^γ . 9 = ((90)/(30))^γ ⇒ 9 = 3^γ . 3^γ = 3² ⇒ γ = 2 . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal W = n R T ln(V₂/V₁), adiabatic P V^γ = const and η