Practice question

**Adiabatic process** no heat exchange Q=0, first law ΔU = -W, for ideal gas P V^γ = constant, T V^{γ-1}= constant, P^{1-γ} T^{γ}= constant, γ = C_p/C_v = (f+2)/f, monatomic γ=5/3, diatomic γ=7/5. Work done W = (P₁V₁ - P₂V₂)/(γ-1), temperature changes due to work. For adiabatic: P₁ V₁^γ = P₂ V₂^γ . 1 × 16^γ = 8 × 4^γ . 16^γ = 8 × 4^γ . ((16)/(4))^γ = 8 ⇒ 4^γ = 8 . 4^γ = 2³ ⇒ 2²γ = 2³ ⇒ 2γ = 3 ⇒ γ = 1.5 . Using first law ΔU = Q - W, W = ∫ P dV, isobaric