A gas is contained in a cyclinder and expands according to the relation `rhoV^(13)`=constant. The initial pressure and initial volume of the gas are 30atm. And 30L respectively. If the final pressure is 15atm, then calculate the work done on the face of piston by the pressure force of the gas.

Options

A. `5xx10^(4)J`
B. `4.36xx10^(4)J`
C. `3xx10^(6)J`
D. `4xx10^(4)J`

Answer

b

Explanation

`W=int_(v_(1))^(2))` pdV and `pV^(1.3)=C.p=CV^(-13)`
`W=int_(v_(1))^(v_(2))CV^(-1/3)dV=(-C)/(0.3)[V^(0.3)]_(v_(1))^(v_(2))`
`C=P_(1)V_(1)^(1.3)=P_(2)V_(2)^(1.3)`
`W=(p_(2)V_(2)-p_(1)V_(1))/(-0.3)`
First volume, `V_(2)=V_(1)((p_(1))/(p_(2)))^(1//1.3)`
`=30xx10^(-3)(2)^(0.77)=30xx10^(-3)xx1.71`
`V_(2)=51.3xx10^(-3)m^(3)`
`W=(15xx10^(5)xx51.3xx10^(-3)-30xx10^(5)xx30xx10^(-3))/(0.3)`
`W=4.36xx10^(4)J`