Page 176 - Advanced Thermodynamics for Engineers, Second Edition

P. 176

CHAPTER

8
EQUATIONS OF STATE

The properties of ﬂuids can be deﬁned in two ways, either by the use of tabulated data (e.g. steam
tables) or by state equations (e.g. perfect gas law). Both of these approaches have been developed by
observation of the behaviour of ﬂuids when they undergo simple processes. It has also been possible to
model the behaviour of such ﬂuids from ‘molecular’ models, e.g. the kinetic theory of gases. A number
of models which describe the relationships between properties for single component ﬂuids, or constant
composition mixtures will be developed here.

8.1 IDEAL GAS LAW
The ideal and perfect gas laws can be developed from a number of simple experiments, or a simple
molecular model. First the experimental approach will be considered.
If a ﬁxed mass of a single component ﬂuid is contained in a closed system then two processes can
be proposed:

1. the volume of the gas can be changed by varying the pressure, while maintaining the temperature
constant;
2. the volume of the system can be changed by varying the temperature, while maintaining the
pressure constant.
The ﬁrst process is an isothermal one, and is the experiment proposed by Boyle to deﬁne Boyle’s
law (also known as Amagat’s law in France). The second process is an isobaric one and is the one used
to deﬁne Charles’ law (also known as Gay-Lussac’s law in France).
The process executed in (1) can be described mathematically as
v ¼ vðpÞ ; (8.1)
T
while the second one, process (2) can be written
v ¼ vðTÞ : (8.2)
p
Since these processes can be undergone independently then the relationship between the three
properties is

v ¼ vðp; TÞ: (8.3)
Equation (8.3) is a functional form of the equation of state of a single component ﬂuid. It can be
seen to obey the two property rule, which states that any property of a single component ﬂuid or

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