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B
Appendix B The mixing equation for ratios
Let us write (2.6) describing the conservation of elements (or isotopes) A and B in the
mixture of components j
=
1, 2,
...
:
C 0
f j C j
=
(B.1)
j
C 0
f j C j
=
(B.2)
j
and then divide one by the other:
C A
C B
f 1 C 1
f 2 C 2
+
+···
0 =
f 1 C 1
f 2 C 2
+
+···
C A
C B
f 1 C 1
=
f 1 C 1
f 2 C 2
+
+···
1
C A
C B
2 +···
f 2 C 2
+
(B.3)
f 1 C 1
f 2 C 2
+
+···
B
B
In the fractions of the right-hand side, we recognize proportions
ϕ
1 ,
ϕ
2 ,
...
,ofthe
denominator element B provided by components 1, 2,
...
, proportions that are written, for
component 1, say:
f 1 C 1
B
1
ϕ
=
(B.4)
f 1 C 1
f 2 C 2
+
+···
Summing the previous equation for all components, it can be verified that the sum of the
various
B
j
ϕ
is equal to unity. We therefore arrive back at (2.9) :
C A
C B
0 =
C A
C B
B
j
ϕ
(B.5)
j
j
 
 
 
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