Numerical Example – Quasisteady State
where c is in ppm and the hydrogen pressure, p
H
, is in atm.
The density of steel is 7.73 g/cm
3
.
The diffusion
coefficient of hydrogen in steel is taken to be 10
8
cm
2
/s.
What is the rate of pressure drop (atm/s) as a result of
diffusion of hydrogen through the wall?
SOLUTION
A cubic steel tank of volume 1 liter and wall thickness 0.1
cm is used to store hydrogen with an initial pressure of 8.7
atm.
The tank is placed in outer space at 673 K.
The
hydrogen concentration
on the steel surface is given by
,
H
p
c
3
=
Diffusion Under an External Field
v – velocity of mass flow or drift velocity under external
force,
F
.
v
c
x
c
D
J
+
∂
∂
−
=
Diffusion
Mass flow or drift due to
an external field
MF
=
v
where
M
is the atom mobility which is related to diffusivity
through the NernstEinstein relation,
T
k
D
M
B
=
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Examples of External Forces, F
ϕ
– elastic potential

d
ϕ
/dx
Elastic potential gradient
γ
– activity coefficient
k
B
Td
(
ln
γ
)
/dx
Gradient of excess chemical
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 Spring '02
 CHEN
 Thermodynamics, edge dislocation, Common Boundary Conditions

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