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A gas is enclosed in a cylinder with a m...

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^-3m^3` changes to a final state at `P_f=(1//32)xx10^5Pa and V_f=8xx10^-3m^3` in an adiabatic quasi-static process, such that `P^3V^3=constant.` Consider another thermodynamic process that brings the system form 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_r.` The amount of heat supplied to the system i the two-step process is approximately

A

112 J

B

294 J

C

588 J

D

813 J

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `gamma= 5/3` (monoatomic gas)
From first law of thermodynamics - `DeltaQ = W + DeltaU`
`implies W = P_(i)DeltaV = 700J`
`DeltaU = nC_vDeltaT = 3/2 [P_fV_f – P_iV_i] = -900/8J`
`DeltaQ=W + DeltaU = 588 J`
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