Pressure equation - Revision history

Carl McBride: Replaced page with a redirect

2012-03-14T14:12:42Z

Replaced page with a redirect

← Older revision		Revision as of 16:12, 14 March 2012
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	~~For particles acting through two-body central forces alone one may use the~~ [[~~Thermodynamic relations \| thermodynamic relation]]~~		#REDIRECT[[Pressure#Pressure equation]]

	~~:<math>p = -\left. \frac{\partial A}{\partial V}\right\vert_T </math>~~

	~~Using this relation, along with the [[Helmholtz energy function]] and the [[partition function \| canonical partition function]], one~~
	~~arrives at the so-called~~
	~~'''pressure~~ equation~~''' (also known as the '''virial equation'''):~~
	~~:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>~~

	~~where <math>\beta := 1/k_BT</math>,~~
	~~<math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential \| potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].~~
	~~==See also==~~
	*[[Virial pressure]]
	~~==References==~~
	~~[[category: statistical mechanics~~]]

Carl McBride: Added internal link

2008-02-27T17:04:32Z

Added internal link

← Older revision		Revision as of 19:04, 27 February 2008
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	:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>		:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>

	where <math>\beta = 1/k_BT</math>,		where <math>\beta := 1/k_BT</math>,
	<math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential \| potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].		<math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential \| potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
			==See also==
			*[[Virial pressure]]
	==References==		==References==
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride at 12:21, 28 June 2007

2007-06-28T12:21:42Z

← Older revision		Revision as of 14:21, 28 June 2007
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	~~The~~ '''pressure equation''', also known as the '''virial equation''' ~~is given by~~		For particles acting through two-body central forces alone one may use the [[Thermodynamic relations \| thermodynamic relation]]
	:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^3~{\rm d}r</math>
			:<math>p = -\left. \frac{\partial A}{\partial V}\right\vert_T </math>

			Using this relation, along with the [[Helmholtz energy function]] and the [[partition function \| canonical partition function]], one
			arrives at the so-called
			'''pressure equation''' (also known as the '''virial equation'''):
			:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>

	where <math>\beta = 1/k_BT</math>,		where <math>\beta = 1/k_BT</math>,

Carl McBride at 13:39, 25 June 2007

2007-06-25T13:39:07Z

← Older revision		Revision as of 15:39, 25 June 2007
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	The '''pressure equation''', also known as the '''virial equation''' is given by		The '''pressure equation''', also known as the '''virial equation''' is given by
	:<math>P^*=\frac{\beta P}{\rho}= \frac{PV}{~~NkT~~} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>		:<math>p^*=\frac{\beta p}{\rho}= \frac{pV}{Nk_BT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^3~{\rm d}r</math>
	where <math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential \| potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
			where <math>\beta = 1/k_BT</math>,
			<math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential \| potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
			==References==
	[[category: statistical mechanics]]		[[category: statistical mechanics]]

Carl McBride at 15:38, 8 June 2007

2007-06-08T15:38:54Z

← Older revision		Revision as of 17:38, 8 June 2007
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	The '''pressure equation''', also known as the '''virial equation''' is given by		The '''pressure equation''', also known as the '''virial equation''' is given by
	:<math>P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>		:<math>P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>
	where <math>\Phi(r)</math> is a ''central'' potential and <math>{\rm g}(r)</math> is the [[pair distribution function]].		where <math>\Phi(r)</math> is a ''central'' [[Intermolecular pair potential \| potential]] and <math>{\rm g}(r)</math> is the [[pair distribution function]].
			[[category: statistical mechanics]]

Carl McBride: New page: The '''pressure equation''', also known as the '''virial equation''' is given by : $P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \f...$

2007-05-22T13:03:02Z

New page: The '''pressure equation''', also known as the '''virial equation''' is given by :<math>P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \f...

New page

The '''pressure equation''', also known as the '''virial equation''' is given by
:<math>P^*=\frac{\beta P}{\rho}= \frac{PV}{NkT} = 1 - \beta \frac{2}{3} \pi \rho \int_0^{\infty} \left( \frac{{\rm d}\Phi(r)} {{\rm d}r}~r \right)~{\rm g}(r)r^2~{\rm d}r</math>
where <math>\Phi(r)</math> is a ''central'' potential and <math>{\rm g}(r)</math> is the [[pair distribution function]].