Practice question

**Gamma determination** γ = C_p/C_v, C_p - C_v = R, for monatomic f=3 C_v=3/2 R C_p=5/2 R γ=1.67, diatomic f=5 C_v=5/2 R C_p=7/2 R γ=1.4, adiabatic relation P V^γ = const allows γ determination from P-V measurements, slope of log P vs log V = -γ. For isochoric: (P₁)/(T₁) = (P₂)/(T₂) . P₁ = 7 atm , T₁ = 40 + 273 = 313 K , T₂ = -20 + 273 = 253 K . (7)/(313) = (P₂)/(253) ⇒ P₂ = (7 × 253)/(313) ≈ 5.66 atm . Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P