Problem Set 2: Difference between revisions

Latest revision as of 16:54, 28 January 2009

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 $\kappa _{T}\;{\sim }\;|T-T_{c}|^{-\gamma }$ .

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-Use the ''Van der Waals equation'' to calculate the critical behavior of:
+) Use the ''[http://en.wikipedia.org/wiki/Van_der_Waals_equation van der Waals equation]'' to calculate the isothermal compressibility <math>\kappa_T = -\frac{1}{V}\left( \frac{\partial V}{\partial P} \right)_T</math>, at <math>T\;  >\;  T_c</math>.
-) the specific heat <math>C_V</math>,
+) Determine its behavior near the critical point, and obtain the corresponding critical exponent <math>\gamma</math>, defined by <math>\kappa_T\; {\sim }\;  |T - T_c |^{-\gamma}</math>.
-) the isothermal compressibility <math>\kappa_T</math>, and
-) the reduced density jump <math>v = | V - V_c |/V_c </math> (across the first order transition line).
-Determine the corresponding critical exponents.

Problem Set 2: Difference between revisions

Latest revision as of 16:54, 28 January 2009

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