Helmholtz energy function: Difference between revisions

Revision as of 18:57, 22 February 2007

A = U - T S

(TS) is a conjugate pair. The differential of this function is

d A = d U - T d S - S d T

d A = T d S - p d V - T d S - S d T

thus one arrives at

d A = - p d V - S d T

leading finally to

A = - k_{B} T \ln Q_{N V T}

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

d A = {(\frac{\partial A}{\partial T})}_{V} d T + {(\frac{\partial A}{\partial V})}_{T} d V

Good for use in the Canonical ensemble.

@@ Line 8: / Line 8: @@
 :<math>\left.dA\right.=dU-TdS-SdT</math>
-but from the [[Second law of thermodynamics]]  one obtains
+From the [[Second law of thermodynamics]]  one obtains
 :<math>\left.dA\right.=TdS -pdV -TdS-SdT</math>
@@ Line 25: / Line 25: @@
 :<math>dA=\left(\frac{\partial A}{\partial T}\right)_V dT + \left(\frac{\partial A}{\partial V}\right)_T dV</math>
-Good for $NVT$
+Good for use in the [[Canonical ensemble]].