Thermodynamic integration: Difference between revisions
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<math>\lambda=0</math>, <math>U_\lambda=U_0</math> and <math>\lambda=1</math>, <math>U_\lambda=U</math> | <math>\lambda=0</math>, <math>U_\lambda=U_0</math> and <math>\lambda=1</math>, <math>U_\lambda=U</math> | ||
:<math>\Delta A = A - A_0 = \int_0^1 d\lambda \langle\frac{\partial U_\lambda}{\partial \lambda}\rangle_{\lambda}</math> | :<math>\Delta A = A - A_0 = \int_0^1 d\lambda \left\langle \frac{\partial U_\lambda}{\partial \lambda} \right\rangle_{\lambda}</math> | ||
where | where | ||
:<math>\left.U_\lambda\right.=(1-\lambda)U_0 + \lambda U</math>. | :<math>\left.U_\lambda\right.=(1-\lambda)U_0 + \lambda U</math>. | ||
==References== | |||
[[category:classical thermodynamics]] | [[category:classical thermodynamics]] | ||
Revision as of 16:30, 29 January 2008
Thermodynamic integration is used to calculate the difference in the Helmholtz energy function between two states. The path must be continuous and reversible. One has a continuously variable energy function 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 U_\lambda} such that 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 \lambda=0} , 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 U_\lambda=U_0} and 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 \lambda=1} , 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 U_\lambda=U}
- 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 \Delta A = A - A_0 = \int_0^1 d\lambda \left\langle \frac{\partial U_\lambda}{\partial \lambda} \right\rangle_{\lambda}}
where
- 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 \left.U_\lambda\right.=(1-\lambda)U_0 + \lambda U} .