In the previous section, the definition of entropy is given by
Rearranging the above equation gives
(1)
The entropy change during an internally reversible process (12) is
Only when the relation between δQ and
T is known, the entropy change can be determined. The relations
between δQ
and T can be found by considering the energy balance of a closed system.
The differential form of the energy balance for a closed system, which
contains a simple substance and undergoes an internally reversible
process, is given by
dU = δQ_{rev}  δW_{rev
} (2)
The
boundary work of a closed system is
δW_{rev} = PdV (3)
Substituting equations (1) and (3) into equation (2) gives
dU = TdS PdV TdS
= dU + PdV
or
Tds = du +Pdv (4)
where
s = entropy per unit mass
Equation (4) is known as the first relation of Tds, or Gibbs
equation.
