Helmholtz energy function: Difference between revisions

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thus one arrives at
thus one arrives at


:<math>\left.dA\right.=-pdV-SdT</math>
:<math>\left.dA\right.=-pdV-SdT</math>.


leading finally to
For ''A(T,V)'' one has the following ''total differential''


:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>
:<math>dA=\left(\frac{\partial A}{\partial T}\right)_V dT + \left(\frac{\partial A}{\partial V}\right)_T dV</math>


The following equation provides a link between [[Classical thermodynamics | classical thermodynamics]] and
[[Statistical mechanics | statistical mechanics]]:


For ''A(T,V)'' one has the following ''total differential''
:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math>
 
:<math>dA=\left(\frac{\partial A}{\partial T}\right)_V dT + \left(\frac{\partial A}{\partial V}\right)_T dV</math>


[[Category: Classical thermodynamics]]
[[Category: Classical thermodynamics]]
Good for use in the [[Canonical ensemble]].
See also the [[Canonical ensemble]].

Revision as of 15:51, 21 May 2007

Hermann Ludwig Ferdinand von Helmholtz Definition of A (for arbeit):

where U is the internal energy, T is the temperature and S is the entropy. (TS) is a conjugate pair. The differential of this function is

From the Second law of thermodynamics one obtains

thus one arrives at

.

For A(T,V) one has the following total differential

The following equation provides a link between classical thermodynamics and statistical mechanics:

See also the Canonical ensemble.