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Question

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi=105 Pa and volume Vi=103m3 changes to a final state at Pf=(1/32)×105 Pa and Vf=8×103m3 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.

A
112 J
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B
294 J
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C
588 J
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D
813 J
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Solution

The correct option is D 813 J
for adiabatic process
P3V3=C
PV5/3=K
r=5/3
wadiabatic=11r(P2V2P1V1)
=1153(132×105×8103105×1103)
=112.5 J
Wisobaric=PΔV
=105×(81)×103
=7×100
=700 J
Wadiabatic+Wisobaric+Wisochoric
112.5+700+0
813 J

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