Spezifisches Volumen

Name

(Massen-)Spezifisches Volumen

$v$

Größen- und Einheitensystem	Einheit	Dimension
SI	m³·kg⁻¹	L³·M⁻¹

Siehe auch: Dichte, Wichte (spezifisches Gewicht), relative Dichte (spezifische Dichte)

Das (Massen-)spezifische Volumen (Formelzeichen $v$ ) ist definiert als Kehrwert der Dichte $\rho$ :^[1]

v={\frac {1}{\rho }}={\frac {V}{m}}

Damit ist das spezifische Volumen das Verhältnis von Volumen $V$ zu Masse $m$ , also das Volumen der Masseneinheit.

Diese intensive Zustandsgröße wird in der Thermodynamik der Gase und Dämpfe und in der Polymer -Analytik verwendet, insbesondere zur Erstellung von Zustandsdiagrammen (Beispiel: p-v-Diagramm).

In der Meteorologie bezeichnet das Formelzeichen α das spezifische Volumen von Luft.^[2]

Molspezifisches Volumen

Wird das Volumen stattdessen auf die Stoffmenge n normiert, so erhält man das molare Volumen $V_{\mathrm {m} }$ , das ebenfalls ein spezifisches Volumen ist:^[1]

V_{\mathrm {m} }={\frac {V}{n}}

Umrechnung

Aus den o. g. Definitionen und der Molmasse $M={\frac {m}{n}}$ folgt:^[1]

V_{\mathrm {m} }={\frac {V}{n}}={\frac {V}{\frac {m}{M}}}=v\cdot M={\frac {M}{\rho }}

Partielles spezifisches Volumen

Das partielle spezifische Volumen ${\bar {v_{i}}}$ der i-ten Komponente einer Lösung ist definiert als die Änderung des Gesamtvolumens ∂V pro Masseneinheit bei Zugabe einer infinitesimalen Menge ∂m_i der Komponente i bei konstantem T und P und den Massen in Gramm, m_j, aller anderen Komponenten.^[3]

{\bar {v_{i}}}=\left({\frac {\partial V}{\partial m_{i}}}\right)_{T,P,m_{j}}{j\neq i}

Sie ist die partielle Ableitung des Volumens nach der Masse der betreffenden Komponente.

Weblinks

Wikibooks: Tabellensammlung – spezifisches Volumen des Wassers – Lern- und Lehrmaterialien

Einzelnachweise

↑ ^a ^b ^c Klaus Langeheinecke, Peter Jany, Gerd Thieleke: Thermodynamik für Ingenieure: ein Lehr- und Arbeitsbuch für das Studium ; mit 57 Tabellen. Springer Science & Business Media, 2008, ISBN 978-3-8348-0418-1, S. 17 (books.google.com).
↑ Michael Hantel: Einführung Theoretische Meteorologie. Springer-Verlag, 2013, ISBN 978-3-8274-3056-4, S. 76 (books.google.com).
↑ Stephen E. Harding, David Scott, Arther Rowe: Analytical Ultracentrifugation: Techniques and Methods. Royal Society of Chemistry, 2007, ISBN 978-1-84755-261-7, S. 390 (books.google.com).

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