One mole of a monatomic gas at pressure 2 atm, 279 K taken to final pressure 4 atm by a reversible path described by P / V = constant. Calculate the magnitude of Δ E w for the process.

Step-by-step solution

dE = dq + dw (F L T) P 1 = K ′ V 1 and P 2 = K ′ V 2 Also V 1 = P 1 K ′ , V 2 = P 2 K ′ T 2 = T 1 P 2 V 2 P 1 V 1 = T 1 P 2 P 2 / K ′ P 1 P 1 / K ′ = T 1 P 2 2 P 1 2 T 2 = T 1 4 2 2 2 = 4 T 1 Δ E = C v Δ T = C v 4 T 1 - T 1 = 3 C v T 1 = 3 3 2 R T 1 = 9 R T 1 2 w = - ∫ v 1 v 2 pdv = - ∫ v 1 v 2 K ′ v dv = - K ′ v 2 2 v 1 v 2 K ′ v 2 = K ′ v v = P v = RT w = - RT 2 T 1 T 2 = - R 2 T 2 - T 1 = - R 2 3 T 1 Δ E w = 9 R T 1 / 2 - 3 R T 1 / 2 = - 3