A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 10^5 Pa and volume Vi = 10^-3 m3 changes to a final state at Pf = (1/32) × 10^5 Pa and Vf = 8 × 10^-3 m3 in an adiabatic quasi-static process, such that P3 V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf. The amount of heat supplied to the system in the two-step process is approximately

Question:

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure P_i = 10⁵ Pa and volume V_i = 10^-3 m³ changes to a final state at P_f = (1/32) × 10⁵ Pa and V_f = 8 × 10^-3 m³ in an adiabatic quasi-static process, such that P3 V5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at P_i followed by an isochoric (isovolumetric) process at volume V_f. The amount of heat supplied to the system in the two-step process is approximately