Yang-Yang anomaly: Difference between revisions
Carl McBride (talk | contribs) (New page: The '''Yang-Yang anomaly''' <ref>[http://dx.doi.org/10.1103/PhysRevLett.13.303 C. N. Yang and C. P. Yang "Critical Point in Liquid-Gas Transitions", Physical Review Letters '''13''' pp. ...) |
Carl McBride (talk | contribs) m (Corrected typo.) |
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Given that experimentally it is found that <math>C_V</math> diverges at the [[Critical points | critical temperature]] this implies that | Given that experimentally it is found that <math>C_V</math> diverges at the [[Critical points | critical temperature]] this implies that | ||
either <math>\partial^2 p/\partial T^2</math> or <math>\partial^2 \mu/\partial T^2</math>, or both, diverge as <math>T \rightarrow T_c^-</math>. | either <math>\partial^2 p/\partial T^2</math> or <math>\partial^2 \mu/\partial T^2</math>, or both, diverge as <math>T \rightarrow T_c^-</math>. | ||
Fisher and Orkoulas <ref>[http://dx.doi.org/10.1103/PhysRevLett.85.696 Michael E. Fisher and G. Orkoulas "The Yang-Yang Anomaly in Fluid Criticality: Experiment and Scaling Theory", Physical Review Letters '''85''' pp. 696-699 (2000)]</ref> showed | Fisher and Orkoulas <ref>[http://dx.doi.org/10.1103/PhysRevLett.85.696 Michael E. Fisher and G. Orkoulas "The Yang-Yang Anomaly in Fluid Criticality: Experiment and Scaling Theory", Physical Review Letters '''85''' pp. 696-699 (2000)]</ref> showed that ''both'' terms diverge. | ||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] | ||
Latest revision as of 16:50, 19 April 2010
The Yang-Yang anomaly [1] provides (Eq. 3):
where is the heat capacity at constant volume and is the chemical potential.
Given that experimentally it is found that diverges at the critical temperature this implies that
either Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \partial^2 p/\partial T^2}
or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \partial^2 \mu/\partial T^2}
, or both, diverge as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T \rightarrow T_c^-}
.
Fisher and Orkoulas [2] showed that both terms diverge.
