Boyle temperature

The Boyle temperature  T _B (named after Robert Boyle ) is the temperature at which a real gas , which is under a small pressure , behaves like an ideal gas .

At the Boyle temperature and low pressures, the pV-p graphs , to which the isotherms correspond in the pressure-volume diagram , run according to Boyle-Mariotte's gas law and are therefore horizontal:

${\displaystyle \lim _{p\to 0}\left({\frac {\partial (pV)}{\partial p}}\right)_{T_{B}}=\lim _{p\to 0}\left({\frac {\partial z}{\partial p}}\right)_{T_{B}}=0}$

With

• p - pressure
• V - volume
• z - compressibility factor .

If one uses the virial equations and ends the approximation with the second term of the series , the Boyle temperature is precisely the temperature at which the second virial coefficient  B vanishes:

${\displaystyle {\begin{aligned}B(T_{B})=b-{\frac {a}{R\cdot T_{B}}}&\approx 0\\\Rightarrow T_{B}&\approx {\frac {a}{b\cdot R}}\end{aligned}}}$

With

• a , b - Van der Waals parameters
• R - general gas constant .

At temperatures T below the Boyle temperature, B (T) is negative:

${\displaystyle T<T_{B}\Rightarrow B(T)<0}$

literature

• Wolfgang Nolting : Basic course in theoretical physics. Part 4: Special Theory of Relativity, Thermodynamics. 7th edition. Springer, Berlin 2010, ISBN 978-3-642-01603-5 .

Individual evidence

1. ↑ Dorothea Lüdecke, Christa Lüdecke: Thermodynamics: Physico-chemical basics of thermal process engineering . 2000, ISBN 3-540-66805-5 ( page 268 in Google book search).
2. ↑ Harry Pfeifer, Herbert Schmiedel, Ralf Stannarius: Compact course in physics . 2013, ISBN 978-3-519-00472-1 ( page 150 in the Google book search).