Helmholtz energy function
Hermann Ludwig Ferdinand von Helmholtz Definition of A (for arbeit):
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.A\right.=U-TS}
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
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.dA\right.=dU-TdS-SdT}
From the second law of thermodynamics one obtains
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.dA\right.=TdS-pdV-TdS-SdT}
thus one arrives at
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.dA\right.=-pdV-SdT} .
For A(T,V) one has the following total differential
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle dA=\left({\frac {\partial A}{\partial T}}\right)_{V}dT+\left({\frac {\partial A}{\partial V}}\right)_{T}dV}
The following equation provides a link between classical thermodynamics and statistical mechanics:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.A\right.=-k_{B}T\ln Q_{NVT}}
See also