Page 497 - Advanced thermodynamics for engineers

20.7 DIFFUSION AND HEAT TRANSFER 489

The specific enthalpy, h, can be related to this parameter by
vðm=TÞ
h ¼ T 2 : (20.99)
vT
Rearranging Eqn (20.99) gives

vðm=TÞ h
¼ : (20.100)
vT p T 2

vðm=TÞ 1 vm
The term ¼ , because T ¼ constant, and from the definition of chemical
vp T vp
T T
potential, m, the term
dm ¼ dg ¼ vdp þ sdT: (20.101)
Thus

vm
¼ v: (20.102)
vp
T

vðm=TÞ vðm=TÞ
Substituting for and in Eqn (20.98) gives
vT vp
p T
h v
dðm=TÞ¼ dT þ dp: (20.103)
T 2 T
Hence from Eqns (20.97) and (20.103)
h v dp L 21 dT
dT þ ¼ (20.104)
T 2 T L 22 T 2
giving

L 21 dT
v dp ¼ h (20.105)
L 22 T
If both vessels were at the same temperature then dT ¼ 0 and
dx
dðm=TÞ

J Q ¼ L 12 T (20.106)
T dx
dðm=TÞ
J m j ¼ L 22 T (20.107)
T
dx
Thus, as shown in Eqn (20.84)

J Q L 12
¼ (20.108)
J m L 22
T

J Q
The ratio is the energy transported when there is no heat flow through thermal conduction.
J m
T

J Q L 21
Also from Onsager’s reciprocal relation ¼ . If this ratio is denoted by the symbol U* then
J m L 22
T
Eqn (20.105) can be written, from Eqn (20.86)