A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure  $P_i={10}^{5}Pa$ and volume  $V_i={10}^{-3}{m}^3$  changes to final state at $P_f=\frac{1}{32}\times {10}^{5}Pa \& V_f=8\times {10}^{-3}{m}^3$ in an adiabatic quasi-static process, such that  $P^3{V}^5=$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