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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>

Revision as of 16:44, 8 June 2007