Modern Thermodynamics
- Chapter 1
to a good approximation, in which U0 is a constant. For monatomic gases such as He and Ar, c=3/2; for
diatomic gases such as N2 and O2, c=5/2. The factor c can be deduced from kinetic theory of gases,
which relates the energy U to the motion of a gas molecules.
The experiments of Gay Lussac, also showed that, at constant pressure, the relative change in
volume (δV/V) due to increase in temperature had nearly the same value for all dilute gases; it was equal
per degree Celsius. Thus a gas thermometer in which the volume of a gas at constant pressure
was the indicator of temperature t, had the quantitative relation:
V = V0(1+ αt) (1.4.9)
in which α =
was the coefficient of expansion at constant pressure. In chapter 3 we will establish
the relation between the temperature t, measured by the gas thermometer, and the absolute temperature T.
The above empirical laws of gases played an important part in the development of
thermodynamics. They are the testing ground for any general principle and are often used to illustrate
these principles. They were also important for developments in atomic theory of matter and chemistry.
For most gases, such as CO2, N2, O2, the ideal gas law was found to be an excellent description
of the experimentally observed relation between p, V and T only for pressures up to about 20 atm.
Significant improvements in the laws of gases did not come till the molecular nature of gases was
understood. In 1873, more than 200 years after Boyle published his famous results, Johannes Diderik van
der Waals (1837-1923), proposed an equation in which he incorporated the effects of attractive forces
between molecules and molecular size on the pressure and volume of a gas. We shall study van der
Waals equation in detail in the next section but here we would like to familiarize the reader with its basic
form so that it could be compared the ideal gas equation. According to van der Waals, p, V, N and T are
related by the equation:
(p + a
) (V Nb) = NRT
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