Mathematical Development
From the first law of thermodynamics we have
- ,
where is the internal energy, is the energy added by heating and is the work done by the system. From the second law of thermodynamics, for a reversible process we may say that . Also, in case of a reversible change, the work done can be expressed as
Applying the product rule for differentiation to d(TS) = TdS + SdT, we have:
- ,
and:
The definition of A = U - TS enables to rewrite this as
This relation is also valid for a process that is not reversible because A is a thermodynamic function of state.
Read more about this topic: Helmholtz Free Energy
Famous quotes containing the words mathematical and/or development:
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“The highest form of development is to govern one’s self.”
—Zerelda G. Wallace (1817–1901)