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:
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)
“The proper aim of education is to promote significant learning. Significant learning entails development. Development means successively asking broader and deeper questions of the relationship between oneself and the world. This is as true for first graders as graduate students, for fledging artists as graying accountants.”
—Laurent A. Daloz (20th century)