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):
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle C_{V}=VT\left.{\frac {\partial ^{2}p}{\partial T^{2}}}\right\vert _{V}-NT\left.{\frac {\partial ^{2}\mu }{\partial T^{2}}}\right\vert _{V}}
where is the heat capacity at constant volume and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \mu }
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.
