Substituting Equation 2.42 into Equation 2.40 and recognizing the fact
that w = −PΔV for an irreversible process at constant pressure leads to
Equation 2.43:
ΔE < TΔS − PΔV
(2.43)
Thus in the above equation, we have deliberately included the condition
of spontaneity in terms of entropy into the first law. Rearranging this
equation gives
ΔE − TΔS + PΔV < 0
(2.44)
or
Δ E − TS + PV
ð
Þ< 0
(2.45)
The variables between the brackets in Equation 2.45 represent a new state
function, which we call the Gibbs energy, G, which we define by Equation
2.46:
G = E − TS + PV
(2.46)
Thus, we see that for a spontaneous irreversible process we have the
condition
ΔG < 0
(2.47)
Instead of using Equation 2.41 for a spontaneous process, we could have
used the ΔS condition for a process at equilibrium; that is
ΔS =
q
T
(2.48)
Following the steps as before, we end up with the condition
ΔG = 0
(2.49)
for a reversible process. In fact, we can use the sign of ΔG to state whether
a particular process at constant pressure will be spontaneous or not under
the given conditions. A positive value of ΔG implies a nonspontaneous
process.
In examining Equation 2.46, we notice that the term E + PV is the state
function H (Equation 2.26). Therefore, we have
G = H − TS
(2.50)
or for any chemical change at a particular temperature T,
ΔG = ΔH − TΔS
(2.51)
THE GIBBS ENERGY STATE FUNCTION
45