Abstract
In this chapter, the basic equations of statistical thermodynamics will be derived for an ideal gas on the basis of Boltzmann approach (Atkins 1986 Moelwin-Hughes 1947).
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Notes
- 1.
\(\ln x! = x\ln x - x = x\ln \frac{x} {e}\).
- 2.
The energy of a system is a function of its volume. As a consequence, the temperature derivatives is calculated at constant volume.
- 3.
Remember that \(\frac{1}{f} \frac{{\rm d}{f}}{\rm dx}=\frac{{\rm dln}f}{\rm dx} \ {\rm and} \ x \frac{{\rm d}{f}}{\rm dx} = \frac{{\rm d}{f}}{{\rm dln}x}\).
- 4.
Applying the Stirling formula reported in note 1.
- 5.
This quantity is related to the molar formation enthalpy in (1.79) by the equation \(\bar{H}\) s f = N a ε s f where N a is the Avogadro number.
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Capitelli, M., Colonna, G., D’Angola, A. (2012). Statistical Thermodynamics. In: Fundamental Aspects of Plasma Chemical Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8182-0_3
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DOI: https://doi.org/10.1007/978-1-4419-8182-0_3
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