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 −3 m 3 changes to a final state at P f ​ =(1/32)x10 5 Pa and V f ​ =8x10 −3 m 3 in an 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.

Options

A. `112J`
B. `294J`
C. `588J`
D. `813J`

Answer

C

Explanation

In adiabatic process `P^(3)V^(5)` = constant
`implies PV^(5//3)` = constant
`implies gamma=(5)/(3) implies C_(V) = (3)/(2)R "and" C_(P) = (5)/(2)R`
In another process

`DeltaQ = nC_(P)DeltaT + nC_(V)DeltaT = (5)/(2)nR (T_(B) - T_(A)) + (3)/(2)nR(T_(C)- T_(B))`
`DeltaQ = (5)/(2)(P_(B)V_(B) - P_(A)V_(A))+ (3)/(2)(P_(C)V_(C) - P_(B)V_(B))`
Putting value
`DeltaQ = 587.5J approx 588J`