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Modern cosmology has established that not only the notion of the
heat death of the universe but also the early attempts to refute the notion
are erroneous: important physical factors—above all, gravitation—were
not taken into account. When gravitation is taken into account, the uniform

isothermal distribution of matter is not at all the most probable distribution
and does not correspond to maximum entropy. Observations show that the
universe is decidedly non-steady state; it is expanding. Matter, which was

nearly uniform at the start of the expansion, with time breaks up into
individual objects, under the action of gravitational forces, forming
galactic clusters, galaxies, stars, and planets. All these processes are
natural, proceed with increasing entropy, and do not require violation of

the laws of thermodynamics. Even in the future, if gravitation is taken into
account, these processes will not lead to a uniform isothermal state of the
universe, i. e., to its heat death. The universe is always no static and

continuously evolving.

CHAPTER 3

Real Gases and Liquids

3.1. Forces and Potential Energy of Molecular Interaction in Gases

In discussions of gases two important assumptions, which are not
always justified, were done. We have assumed that the volume of the

molecules themselves is negligible in comparison with the total space
occupied by the gas and that the attractive forces between gas molecules
are negligible. For experiments with gases such as oxygen and hydrogen at

room temperature and ordinary pressures, these assumptions are justified.
But at high pressure these assumptions are not valid and deviations from
laws of ideal gas take place. For the ideal gases the factor of compression

is the following

pV
 (3.1.1)
 RT
in accordance with Mendeleev-Klapeiron equation pV  RT . But for

real gases the factor of compression depends on the pressure and

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