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A fixed mass of gas is taken through a p...

A fixed mass of gas is taken through a process `A rarr B rarr C rarrA`. Here `A rarr B` is isobaric, `B rarr C` is adiabatic and `C rarr A `is isothermal. Find pressure at `C`

.

A

`(10^(5))/( 64) N //m^(2)`

B

`(10^(5))/( 32) N //m^(2)`

C

`(10^(5))/( 12) N //m^(2)`

D

`(10^(5))/( 6) N //m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
a For adiabatic process `BC`,
`P_(B)=P_(C)` ...(i)
For isothermal process `CA`
`P_(A)V_(A)=P_(C)V_(C)` ...(ii)
From Eqs. (i) and (ii)
`V_(C)=[(V_(B)^(gamma))/(V_(A))]^((1)/( gamma-1))=64m^(3)`
`P_(C)=(P_(A)V_(A))/(V_(C))=(10^(5))/( 64)N//m^(2)`
b Work done, `W=W_(AB)+W_(BC)+W_(CA)`
`=P(V_(B)-V_(A))+(1)/(gamma-1)[PV_(B)-P_(C)V_(C)+PV_(A)1n(V_(A)//V_(C))]`
Putting the values,
`W=4.9 xx 10^(5)J`
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