A substance for which is a constant undergoes an isothermal, mechanically reversible process from initial state

A substance for which κ is a constant undergoes an isothermal, mechanically reversible process from initial state (P₁, V₁) to final state (P₂, V₂), where V is molar volume.
(a) Starting with the definition of κ, show that the path of the process is described by: 

V = A (T) exp (−κP)
(b) Determine an exact expression which gives the isothermal work done on 1 mol of this constant-κ substance.