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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
` = n R/(gamma -1) gamma Delta T = (gamma P Delta V)/(gamma -1) =((5/3))/((5/3 -1)) 1^(5) (7xx10^(2)) = 5/2 xx7xx10^2 = 35/2 xx10^2 J`
`Delta Q_2 = nC_V Delta T = (nR)/(gamma -1) DeltaT = ((DeltaP)V)/(gamma -1) = ((1/32 -1)10^5 xx8xx10^-3)/(5/3-1) = (-13)/32 xx(8xx10^2)/2 xx3 =(-93)/8 xx10^2 J`
`Delta Q =Delta Q_1 + Delta Q_2 =(35/2 - 93/8)xx10^2, " "Delta Q_2 = (140o-93)/8 xx100 = 4700/8 = 587.5 "joule "`
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