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low compressibility of the liquid. Segments ad and ec belong to
superheated liquid and supercooled vapor respectively (metastable states).
Segment de is physically unrealized because here there is a volume
increase with an increase in pressure. The set of points a , a′ , a″, … and c

c′ , c″ , … determines a curve, called a binodal, which outlines the region
of simultaneous existence of gas and liquid. At the critical point-C the
temperature, pressure, and volume (T , p , and V ) have values that are
c
c
c
characteristic of each substance. However, if the relative values T  T
T c R
p V
,  p , and  V are introduced into van der Waals’ equation,
p c R V c R

then it is possible to obtain the so-called reduced van der Waals’ equation,
which is universal — that is, it does not depend on the individual

properties of the substance.

3
p ( R  )  3 ( V  )1  Т  8 R (3.2.11)
R
V R 2

3.3 Internal Energy of the Real Gas. Joule-Thomson Effect

Internal energy of ideal gas is determined only by kinetic energy of

motion of its molecules. In the real gases interaction between molecules
determine potential energy. Therefore, internal energy of the real gas
consists of kinetic energy of chaotic motion of molecules and potential
energy of intermolecular interaction

U  E  E (3.3.1)
p
k

If total internal energy of the real gas does not change, then

E  E 0  dU   dU (3.3.2)
p
p
k
k
If we take into account that U  C V T , we can write
k

C  dT  dE  0  C  dT   dU . (3.3.3)
V
V
П
П
R

It means, we have to change potential energy of intermolecular

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