Modern Engineering Thermodynamics

364 CHAPTER 11: More Thermodynamic Relations
Differentiating this equation gives
but from Eq. (11.1) we have
so that
df = du − Tds− sdT
du − Tds= −pdv
df = −pdv− sdT (11.5)
If we presume the existence of a functional relation of the form
then its total differential is
df =
f = fðv, TÞ
∂f
∂v
dv +
T
∂f
∂T
dT (11.6)
v
and, on comparing Eqs. (11.5) and (11.6), we see that
and
p = − ∂f
∂v
T
s = − ∂f
∂T
v
The second new thermodynamic function is the total Gibbs function G, named after the American physicist
Josiah Willard Gibbs (1839–1903), defined as
G = H − TS
Dividing by the system mass gives the specific Gibbs function g as
Differentiating Eq. (11.7) gives
but from Eq. (11.3), we have
so that
If we presume a functional relation of the form
g = h − Ts (11.7)
dg = dh − Tds− sdT
dh = Tds+ vdp
dg = vdp− sdT (11.8)
g = gðp, TÞ
then its total differential is
and comparing Eqs. (11.8) and (11.9) gives
and
dg =
∂g
∂p
dp +
T
v =
∂g
∂p
∂g
∂T
T
s = − ∂g
∂T
p
dT (11.9)
p