Problem Set 2

Critical behavior at the liquid-gas critical point

1) Use the van der Waals equation to calculate the isothermal compressibility $\kappa _{T}=-{\frac {1}{V}}\left({\frac {\partial V}{\partial P}}\right)_{T}$, at $T\;>\;T_{c}$.

2) Determine its behavior near the critical point, and obtain the corresponding critical exponent $\gamma$, defined by $\kappa _{T}\;{\sim }\;|T-T_{c}|^{-\gamma }$.