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:
“All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
—Roger Bacon (c. 1214–c. 1294)
“Information about child development enhances parents’ capacity to respond appropriately to their children. Informed parents are better equipped to problem-solve, more confident of their decisions, and more likely to respond sensitively to their children’s developmental needs.”
—L. P. Wandersman (20th century)