Solutions to Homework #1
Problem #1.
(Similar problem with a different geometry was solved in example 1(problem 1), so I will try to
make it short)
Assuming steady state condition, we can calculate the total flux(in moles/sec) of hydrogen
through the surface of spherical tank as,
J
D
r
dc
dr
dc
dr
M
p
Fe
total
H
= 
≈


.(
).
.( /
).
.
.
4
2
0
10
5
1
0 01
2
π
ρ
where
'p' is pressure of hydrogen in the tank in MPa,
'M' is the molecular weight of hydrogen in gm/mole,
'
ρ
' is the density of iron in g/cm
3
,
'r' is the inner radius of the spherical tank.
Flux out of the tank (in moles/sec) is same as rate of loss of hydrogen (in moles) from the tank.
Assuming ideal gas behavior for hydrogen, PV = nRT
J
dn
dt
V
RT
dP
dt
total
=
=
If we use proper units for 'R' and 'V', then dP/dt is approx. 650 Pa/s.
Problem #2.
The quantity 'a' in counts/s/mg is a measure of tracer concentration in different sections.
Plot ln a (logarithm to the base e) vs. x
2
in cm
2
and fit a least square linear line to the data. The
slope of the linear fit is
(1/4Dt). Knowing that t=20hr, we can find the diffusion coefficient.
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 Spring '02
 CHEN
 Trigraph, Boron, concentration profile

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