Editing Helmholtz energy function
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[[Hermann Ludwig Ferdinand von Helmholtz]] | |||
Definition of | Definition of A (for ''arbeit''): | ||
:<math>A | :<math>\left.A\right.=U-TS</math> | ||
''(TS)'' is a ''conjugate pair''. The differential of this function is | ''(TS)'' is a ''conjugate pair''. The differential of this function is | ||
:<math>\left.dA\right.=dU-TdS-SdT</math> | :<math>\left.dA\right.=dU-TdS-SdT</math> | ||
From the [[Second | From the [[Second law of thermodynamics]] one obtains | ||
:<math>\left.dA\right.=TdS -pdV -TdS-SdT</math> | :<math>\left.dA\right.=TdS -pdV -TdS-SdT</math> | ||
Line 15: | Line 14: | ||
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 | |||
:<math>\left.A\right.=-k_B T \ln Q_{NVT}</math> | :<math>\left.A\right.=-k_B T \ln Q_{NVT}</math> | ||
For ''A(T,V)'' one has the following ''total differential'' | |||
:<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]]. |