One mole of an ideal gas at a temperature `T_(1)` expands according to the law `(p)/(V)=` a constant.Findthe work donw when the final temperature is `T_(2)`

Answer

`(1)/(2)r(T_(2)-T_(1))`

Explanation

`(p)/(V)= a constatn = k`
initial temperature - `T_(1) `
Final temperature - `T_(2)`
`W = intPdv`
`W=overset(V_2)underset(V_i)intkvdv`
`W = (k(V_(2)^(2)-V_(1)^(2)))/(2)`
`P_(2) = kV_(2),P_(1) =kV_(1)`
`W = (P_(2)V_(2)-P_(1)V_(1))/(2) =(R(T_(2)-T_(1)))/(2)`