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

Options

A. `122J`
B. `294J`
C. `588J`
D. `813J`

Answer

C

Explanation

`PV^(5/3)=` constant `gamma=(5)/(3)`
`Q_(1)=nC_(p)DeltaT=nC_(p)(PDeltaV)/(nR)`
`Q_(1)=17.5xx10^(2)J`
`Q_(2)=nC_(v)DeltaT=nC_(v)(V_(f)DeltaP)/(nR)=-(93)/(8)xx10^(2)J`
`Q_("net")=Q_(1)+Q_(2)=587.5J`