Two identical containers contain same amount of ideal gas at identical condition. Gas is one container is expanded to 4 times of its volume at constant pressure and gas in another container is expanded to four times to its volume by isothermal process. If `W_(1)` and `W_(2)` be the respective work done, then `(W_(1))/(W_(2))=(alpha)/(In2)`. Find `2/3 alpha`

Answer

1

Explanation

`P_(0)V_(0)=nRT_(0)`
`W_(1)=P_(0)(4V_(0)-V_(0))=3nRT_(0)`
`W_(2)=mRT_(0) In 4=2nRT_(0) In 2`
`(W_(1))/(W_(2))=(3nRT_(0))/(2nRT_(0) In2)=3/(2In2)impliesalpha=3/2implies2/3alpha=1`