Assuming that the volume of a solid or liquid was independent of the external pressure, we deduced that there was no change in the Gibbs free energy of a solid or liquid when the pressure is changed. In fact the volume of a sample does change when subjected to pressure, and we ought to see how to take this effect into account, and then judge whether (or not) it is significant. The volume varies in a way that can be determined by specifying the isothermal compressibility \(k=-(1/V)(\frac{\partial V}{\partial P})_{T}\)  and we assume that k is virtually constant over a pressure range of interest. (this is still an approximation, but it is a better approximation than assuming that the volume itself is constant) Obtain an expression for the Gibbs free energy \(P_{f}\) in terms of its value at \(P_{i}\) , the original volume and the isothermal compressibility.