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

A Calculations A.2. Mass spectrometer inlet volume
Calculation of the sample tube volume
The inner volume of the copper sample tubes is calculated using an empirical formula by Wieser
[2006], who characterized the relation of length to volume of copper tubes of the same kind,
squeezed shut using the same method as applied here. The inner volume is calculated from the
length of the copper tube, measured after the sample was extracted:
• L : length of the sample tube
• A = (−0.12284 ± 0.00336) cm 3 : empirical parameter
• B = (0.13583 ± 6.35 × 10 −4 ) cm 2 : empirical parameter
Gaussian error propagation
(∆n(L)) 2 =
V (L)[cm 3 ] = B · L[cm] + A (A.6)
�
V (L)
· ∆psample
(T + 273.15) · R · 10000
�
psample − pH2O
+
· ∆V (L)
(T + 273.15) · R · 10000
A.2 Mass spectrometer inlet volume
� 2
� 2
�
V (L)
+
· ∆pH2O
(T + 273.15) · R · 10000
�
psample − pH2O
+
(T + 273.15) 2 · ∆T
· R · 10000
The volume of the mass spectrometer inlet was volumetrically measured, using the following set
of previously measured [T. Marx, personal note] volumes:
V1 = (38, 876 ± 0, 470) ml
Vkl = (77, 338 ± 0, 040) ml
Volumes V1 and Vkl were connected and flooded with atmospheric air at pressures between 1 and
11 mbar. The inlet volume Vinlet and the unknown volume V2 connecting Vinlet and (V1+Vkl) were
evacuated. All volumes were at the same temperature when the gas was expanded successively
into the evacuated volumes. The pressures p1, p2 and p3 correspond to the volumes (V1 + Vkl),
(V1 + Vkl + V2) and (V1 + Vkl + V2 + Vinlet) respectively. The inlet volume is then calculated using
the following equation:
p1(V1 + Vkl) = p2 [(V1 + Vkl) + V2]
� �
p1
⇒ V2 = (V1 + Vkl) − 1
p1(V1 + Vkl) = p3 [(V1 + Vkl) + V2 + VC]
77
p2
� 2
� 2