dU = δQ + δW
dU is the infinitesimal change in internal energy
δQ is the infinitesimal heat or thermal energy
δW is the infinitesimal work
dU is an
exact differential
δQ and δW
are inexact differentials
inexact differentials often relate to
irreversible processes
δQ = 0
is an adiabatic process
quasistatic process
a series of infinitesimal equilibrium states/changes
δW =
-PdV
recipproal theorem
(dx/dy)z = (dy/dx)^-1 z
reciprocity theorem
(dx/dy)z (dy/dz)x (dz/dx)y = -1
the chain rule of differentiation
(dx/dz)g = (dx/dy)g (dy/dz)g
definition of a non-natural derivative
take a derivative with respect to a variable and keep another variable fixed, which is not one of the natural derivatives