Ideal gas Helmholtz energy function - Revision history

Carl McBride: defined a couple of terms

2008-08-04T10:19:32Z

defined a couple of terms

← Older revision		Revision as of 12:19, 4 August 2008
Line 13:		Line 13:
	:<math>A=Nk_BT\left(\ln \Lambda^3 \rho -1 \right)</math>		:<math>A=Nk_BT\left(\ln \Lambda^3 \rho -1 \right)</math>

			where <math>\Lambda</math>is the [[de Broglie thermal wavelength]] and <math>k_B</math> is the [[Boltzmann constant]].
	[[Category:Ideal gas]]		[[Category:Ideal gas]]
	[[Category:Statistical mechanics]]		[[Category:Statistical mechanics]]

Carl McBride at 15:44, 8 June 2007

2007-06-08T15:44:00Z

← Older revision		Revision as of 17:44, 8 June 2007
Line 1:		Line 1:
	From equations		From equations
	:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>		:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>
	and		for the [[ Ideal gas partition function \| canonical ensemble partition function for an ideal gas]], and
	:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>		:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>
	one has		for the [[Helmholtz energy function]], one has
	:<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}{\Lambda^{3}}\right)</math>		:<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}{\Lambda^{3}}\right)</math>
	::<math>=-k_BT\left(-\ln N! + N\ln\frac{VN}{\Lambda^3N}\right)</math>		::<math>=-k_BT\left(-\ln N! + N\ln\frac{VN}{\Lambda^3N}\right)</math>

Nice and Tidy at 11:05, 27 February 2007

2007-02-27T11:05:30Z

← Older revision		Revision as of 13:05, 27 February 2007
Line 11:		Line 11:
	one arrives at		one arrives at

	<math>A=Nk_BT\left(\ln \Lambda^3 \rho -1 \right)</math>		:<math>A=Nk_BT\left(\ln \Lambda^3 \rho -1 \right)</math>

			[[Category:Ideal gas]]
			[[Category:Statistical mechanics]]

Carl McBride at 14:20, 21 February 2007

2007-02-21T14:20:04Z

← Older revision		Revision as of 16:20, 21 February 2007
Line 2:		Line 2:
	:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>		:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>
	and		and
	:<math>A=-k_B T \ln Q_{NVT}</math>		:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>
	one has		one has
	:<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}{\Lambda^{3}}\right)</math>		:<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}{\Lambda^{3}}\right)</math>

Carl McBride: New page: From equations : $Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N$ and : $A=-k_B T \ln Q_{NVT}$ one has : $A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}...$

2007-02-21T12:04:38Z

New page: From equations :<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math> and :<math>A=-k_B T \ln Q_{NVT}</math> one has :<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}...

New page

From equations
:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>
and
:<math>A=-k_B T \ln Q_{NVT}</math>
one has
:<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}{\Lambda^{3}}\right)</math>
::<math>=-k_BT\left(-\ln N! + N\ln\frac{VN}{\Lambda^3N}\right)</math>
::<math>=-k_BT\left(-\ln N! + N\ln\frac{N}{\Lambda^3 \rho}\right)</math>
using [[Stirling's approximation]]
:<math>=-k_BT\left( -N\ln N +N + N\ln N - N\ln \Lambda^3 \rho \right)</math>
one arrives at

<math>A=Nk_BT\left(\ln \Lambda^3 \rho -1 \right)</math>

Ideal gas Helmholtz energy function - Revision history

Carl McBride: defined a couple of terms

Carl McBride at 15:44, 8 June 2007

Nice and Tidy at 11:05, 27 February 2007

Carl McBride at 14:20, 21 February 2007

Carl McBride: New page: From equations :Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N and :A=-k_B T \ln Q_{NVT} one has :A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}...

Carl McBride: New page: From equations : $Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N$ and : $A=-k_B T \ln Q_{NVT}$ one has : $A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}...$