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A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure \( P_{i}=10^{5} \mathrm{~Pa} \) and volume \( V_{i}=10^{-3} \mathrm{~m}^{3} \) changes to a final
\( \mathrm{P} \) state at \( P_{f}=(1 / 32) \times 10^{5} \mathrm{~Pa} \) and \( V_{f}=8 \times 10^{-3} \mathrm{~m}^{3} \) in an W 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
[JEE 2016]
(a) \( 112 \mathrm{~J} \)
(b) \( 294 \mathrm{~J} \)
(c) \( 588 \mathrm{~J} \)
(d) \( 813 \mathrm{~J} \)
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