A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $$Pi=105Pa$$ and volume $$Vi=10$$−$$3m3$$ changes to final state at $$Pf=132$$×$$105Pa$$ & $$Vf=8$$×$$10$$−$$3m3$$ in an adiabatic $$quasi-static$$ process, such that $$P3V5=constant$$. 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  $$Pi=105Pa$$ and volume  $$Vi=10$$−$$3m3$$  changes to final state at $$Pf=132$$×$$105Pa$$  &  $$Vf=8$$×$$10$$−$$3m3$$ in an adiabatic $$quasi-static$$ process, such that  $$P3V5=constant$$. 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

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Case $$1$$ : $$PV53=constant$$​⇒γ$$=53$$ , Monoatomic gas​Process is adibatic.​$$W=PfVf$$−$$PiVi1$$−γ$$=132$$×$$105$$×$$8$$×$$10$$−$$3$$−$$105$$×$$10$$−$$31$$−$$53=112.5J$$​⇒△$$U=$$−$$W=$$−$$112.5JCase$$ $$2$$ : ​$$Wisobaric=PiVf$$−$$Vi=1058$$×$$10$$−$$3$$−$$10$$−$$3=700J$$​$$Wisochoric=0$$​⇒$$Wnet=700J$$​First law of thermodynamics,​$$Q=$$△$$U+Wnet=$$−$$112.5+700=587.5J=588$$ J nearly

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