Find the expression for the work done by a system undergoing isothermal compression (or expansion) form volume `V_(1)` to `V_(2)` at temperature `T_(0)` for a gas which obeys the van der wattws equation of state. `(P +an^(2) //V^(2)) (V-bn) =nRT`?

Answer

`nRT_(0)ln ((V_(2)-nb)/(V_(1)-nb)) +an^(2) ((V_(1)-V_(2))/(V_(1)V_(2)))`

Explanation

`p = (nRT)/((V-bn)) - (an^(2))/(V^(2))`
work done by ststem `= int pdV`
`= overset(V_(2))underset(V_(1))int ((nRT_(0))/(V-bn)-(an^(2))/(V^(2)))dV`
`= nRT_(0) overset(V_(2))underset(V_(1)) int (1)/(V-bn) dV - an^(2) overset(V_(2))underset(V_(1))int (dV)/(V^(2))`
`W = nRT_(0) ln ((V_(2)-nb)/(V_(1)-nb)) +an^(2)((V_(1)-V_(2))/(V_(1)V_(2)))`