The work done by one mole of an ideal gas in the reversible process: PV^3 = constant, from (1 atm, 3 — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Polytropic process with x = 3. P1 = 1 atm, T1 = 300 K, P2 = 2√2 atm = 2^1.5 atm. For PV^3 = constant: T^3 / P^2 = constant => (T2/T1)^3 = (P2/P1)^2 = (2^1.5)^2 = 8 => T2/300 = 2 => T2 = 600 K. The work done in a polytropic process is w = nR * (T2 - T1) / (x - 1). For n = 1, x = 3, w = 1 * R * (600 - 300) / (3 - 1) = 150 R.