Geoscience Reference
In-Depth Information
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
0
=
C
A
C
B
B
j
ϕ
(B.5)
j
j