A closed system contains 2.50 mol of oxygen gas (O2), treate…
A closed system contains 2.50 mol of oxygen gas (O2), treated as a diatomic ideal gas with constant molar heat capacities. The gas undergoes the following four-step cycle:Step 1 → 2: isobaric expansion. The gas initially is at P1 = 10.0 bar and V1 = 2.00 L and expands at constant pressure until V2 = 8.00 L.Step 2 → 3: reversible isothermal expansion. The gas expands isothermally at T2 = T3 until its volume doubles to V3 = 16.0 L.Step 3 → 4: isochoric cooling. The system is cooled at constant volume (V3 = V4) to a lower pressure.Step 4 → 1: adiabatic compression. The system is compressed reversibly and adiabatically back to the initial state (P1, V1).Use R = 8.314 J mol⁻¹ K⁻¹ = 0.08314 L·bar mol⁻¹ K⁻¹. Assume ideal-gas behavior and temperature-independent heat capacities.a) Calculate the temperatures T1, T2, T3, and T4. (2 points)b) For each step (1→2, 2→3, 3→4, 4→1), calculate the heat Q, the work W, the change in internal energy ΔU, and the change in enthalpy ΔH. (16 points)c) Sketch a P–V diagram with the numerical state points and indicate the direction of the cycle. (3 points)