Diploma thesis in Physics submitted by Florian Freundt born in ...

A.3. Fractionation-Values A Calculations
For the measured pressures see Table B.6.
Gaussian error propagation
(∆V2) 2 =
(∆Vinlet) 2 =
�� p1
p2
A.3 Fractionation-Values
⇒ Vinlet = p1
(V1 + Vkl) − (V1 + Vkl) − V2
p3
�
p1
= (V1 + Vkl) − 1 −
p3
p1
�
+ 1
p2
� �
p1
= (V1 + Vkl)
� �2 ��
p1
− 1 ∆V1 +
p2
p3
− p1
p2
� �2 − 1 ∆Vkl
�� � �2 ��
(V1 + Vkl) +
∆p1 + −
p2
(V1 + Vkl)p1
p2 2
� �2 ∆p2
��
p1
−
p3
p1
� �2 ��
p1
∆V1 + −
p2
p3
p1
� �2 ∆Vkl
p2
��
(V1 + Vkl) +
−
p3
(V1
� �2 ��
+ Vkl) ∆p1 + −
p2
(V1 + Vkl)p1
p2 2
� �2 ∆p2
��
+ − (V1 + Vkl)p1
p3 2
� �2 ∆p3
The Fractionation-Values are calculated based on Kendrick et al. [2006], but use 40 Ar instead
of 36 Ar as the reference isotope, since in this study’s environment, influences by radiogenic 40 Ar
are negligible.
F X =
�
X
�
�
40Ar sample
� X
�
40Ar air
(A.7)
where X stands for the noble gas isotopes. The F-Value define a mixing line between atmospheric
composition and measured composition, if a sample noble gas isotope has an F-Value of 1 its
volume mixing ratio equals that of atmospheric air.
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