Work done during isothermal volume change (in one step) under a constant external pressure (isothermal irreversible process) is given by

Options

A. `w = P_(ex) Delta V`
B. `w = - P_(ex) Delta V`
C. `w = V Delta P_(ex)`
D. `w = - V Delta P_(ex)`

Answer

B

Explanation

`dw = - P_(ex) dV`
`w = - int_(V_(i))^(V_(f)) P_(ex) dV = - P_(ex) int_(V_(i))^(V_(f)) dV = - P_(ex) Delta V`
The sign convertion for work is that `w` is positve for work done on the system by the sourroundinga and negative for work done by system on the surrounding. Never make the error of setting work equal to `V Delta P`.