JEE (Advanced) 2016 Paper-2 Question 3

Question 3

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 a final state at $$P_f = \left(\frac{1}{32}\right) \times 10^5 Pa$$ and $$V_f = 8 \times 10^{-3} m^3$$ in an adiabatic quasi-static process, such that $$P^3V^5$$ = 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

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