A gas is expanded to double its volume by two different processes. One is isobaric and the other is isothermal. Let `W_(1)` and `W_(2)` be the respective work done, then find `W_(1)` and `W_(2)`

Options

A. `W_(2) = W_(1) ln(2)`
B. `W_(2) = (W)/(ln(2))`
C. `W_(2) =(W_(1))/(2)`
D. data is insufficient

Answer

A

Explanation

`W_(1) = PdV = P (V_(2) - V_(1))`
`rArr W_(1) = PV_(1) ((V_(2))/(V_(1)) - 1)`
`= nRT (2-1) = nRT`
`W_(2) = nRT ln'(V_(2))/(V_(1)) nRT ln 2`
`W_(2) = W_(1) ln2`