Second law of thermodynamics: Difference between revisions
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:<math>\left.dU\right.=TdS -PdV</math> | :<math>\left.dU\right.=TdS -PdV</math> | ||
where <math>U</math> is the [[internal energy]]. | |||
For an open system: | For an open system: | ||
:<math>\left.dU\right.=TdS -PdV + \mu dN</math> | :<math>\left.dU\right.=TdS -PdV + \mu dN</math> | ||
where <math>\mu</math> is the [[chemical potential]]. | |||
For <math>U(S,V)</math> one has the following total differential | For <math>U(S,V)</math> one has the following total differential | ||
Revision as of 11:20, 29 May 2007
For a reversible change
- 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.dQ\right.=TdS}
Thus for a closed system (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 n} fixed):
- 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.dU\right.=TdS -PdV}
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 U} is the internal energy. For an open system:
- 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.dU\right.=TdS -PdV + \mu dN}
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 \mu} is the chemical potential.
For 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(S,V)} one has the following total differential
- 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 dU=\left(\frac{\partial U}{\partial S}\right)_V dS + \left(\frac{\partial U}{\partial V}\right)_S dV}