Problem Set 2: Difference between revisions

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'''Critical behavior at the liquid-gas critical point'''
'''Critical behavior at the liquid-gas critical point'''


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


1) the specific heat <math>C_V</math>,
1) 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>.


2) the isothermal compressibility <math>\kappa_T</math>, and


3) the reduced density jump <math>v = | V - V_c |/V_c </math> (across the first order transition line).


Determine the corresponding critical exponents, defined by <math>v ~ |T - T_c |</math>
2) 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>.

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 , at .


2) Determine its behavior near the critical point, and obtain the corresponding critical exponent , defined by .

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