Practice question

**Energy transfer** first law ΔU = Q - W, W includes P-V work, shaft work, electrical work, Q includes conduction Fourier law, convection, radiation Stefan-Boltzmann, distinction important because work is controllable, heat spontaneous from hot to cold, entropy associated with heat not work, explaining why heat engine efficiency <100%. For adiabatic: P₁ V₁^γ = P₂ V₂^γ . 15 × 28^γ = 3 × 84^γ . 15 / 3 = ((84)/(28))^γ ⇒ 5 = 3^γ . γ = (log(5))/(log(3)) ≈ 1.465 ≈ 1.5 (standard value from context). Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV, isothermal