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`.

Options

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)`

Answer

A

Explanation

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`