Problem Set 2: Difference between revisions

Revision as of 23:14, 19 January 2009

Critical behavior at the liquid-gas critical point

Use the Van der Waals equation to calculate the critical behavior of:

1) The isothermal compressibility $\kappa _{T}=\left({\frac {\partial V}{\partial P}}\right)_{T}$ , at $T>T_{c}$ ;

2) The reduced density jump $\delta V=|V-V_{c}|/V_{c}$ (across the first order transition line), at $T>T_{c}$ .

Determine the corresponding critical exponents.

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 Use the ''Van der Waals equation'' to calculate the critical behavior of:
-) the specific heat <math>C_V</math>,
+) The isothermal compressibility <math>\kappa_T = \left( \frac{\partial V}{\partial P}\right)_T</math>, at <math>T > T_c</math>;
-) the isothermal compressibility <math>\kappa_T</math>, and
+) The reduced density jump <math>\delta V = | V - V_c |/V_c </math> (across the first order transition line), at <math>T > T_c</math>.
-) the reduced density jump <math>v = | V - V_c |/V_c </math> (across the first order transition line).
 Determine the corresponding critical exponents.