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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

From equations

for the canonical ensemble partition function for an ideal gas, and

for the Helmholtz energy function, one has

using Stirling's approximation

one arrives at