Pressure: Difference between revisions
Carl McBride (talk | contribs) (New page: The '''pressure''' is given by :<math>p = - \left.\frac{\partial A}{\partial V} \right\vert_{T,N} = kT \left.\frac{\partial \ln Q}{\partial V} \right\vert_{T,N}</math> where <math>A</mat...) |
Carl McBride (talk | contribs) m (Slight tidy.) |
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'''Pressure''' (<math>p</math>) is the force per unit area applied on a surface, in a direction perpendicular to that surface, i.e. the scalar part of the [[stress]] tensor. The SI units for pressure are Pascals (Pa). | |||
In thermodynamics the pressure is given by | |||
:<math>p = - \left.\frac{\partial A}{\partial V} \right\vert_{T,N} = | :<math>p = - \left.\frac{\partial A}{\partial V} \right\vert_{T,N} = k_BT \left.\frac{\partial \ln Q}{\partial V} \right\vert_{T,N}</math> | ||
where <math>A</math> is the [[Helmholtz energy function]], <math>V</math> is the volume and <math>Q (N,V,T)</math> | where <math>A</math> is the [[Helmholtz energy function]], <math>V</math> is the volume, <math>k_B</math> is the | ||
[[Boltzmann constant]], <math>T</math> is the [[temperature]] and <math>Q (N,V,T)</math> | |||
is the [[Canonical ensemble | canonical ensemble partition function]]. | is the [[Canonical ensemble | canonical ensemble partition function]]. | ||
==See also== | ==See also== | ||
Revision as of 11:16, 31 January 2008
Pressure (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 p} ) is the force per unit area applied on a surface, in a direction perpendicular to that surface, i.e. the scalar part of the stress tensor. The SI units for pressure are Pascals (Pa). In thermodynamics the pressure is given by
- 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 p = - \left.\frac{\partial A}{\partial V} \right\vert_{T,N} = k_BT \left.\frac{\partial \ln Q}{\partial V} \right\vert_{T,N}}
where is the Helmholtz 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 V} is the volume, 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 k_B} is the Boltzmann constant, 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} is the temperature 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 Q (N,V,T)} is the canonical ensemble partition function.
