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Difference between revisions of "Ideal gas Helmholtz energy function"

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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>
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:<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]]

Latest revision as of 11:19, 4 August 2008