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Equations of state
1.1
The perfect gas equation of state
1.2
Using the perfect gas law
Box 1.1 The gas laws and the weather
1.3
Mixtures of gases: partial pressures
The kinetic model of gases
1.4
The pressure of a gas according to
the kinetic model
1.5
The average speed of gas molecules
1.6
The Maxwell distribution of speeds
1.7
Diffusion and effusion
1.8
Molecular collisions
Real gases
Box 1.2 The Sun as a ball of perfect gas
1.9
Molecular interactions
1.10 The critical temperature
1.11 The compression factor
1.12 The virial equation of state
1.13 The van der Waals equation of state
1.14 The liquefaction of gases
CHECKLIST OF KEY IDEAS
FURTHER INFORMATION 1.1
DISCUSSION QUESTIONS
EXERCISES
Chapter 1
The properties of gases
Although gases are simple, both to describe and in
terms of their internal structure, they are of immense
importance. We spend our whole lives surrounded
by gas in the form of air, and the local variation
in its properties is what we call the ‘weather’. To
understand the atmospheres of this and other planets
we need to understand gases. As we breathe, we
pump gas in and out of our lungs, where it changes
composition and temperature. Many industrial
processes involve gases, and both the outcome of
the reaction and the design of the reaction vessels
depend on a knowledge of their properties.
Equations of state
We can specify the state of any sample of substance
by giving the values of the following properties (all
of which are deﬁned in the
Introduction
):
V
, the volume of the sample
p
, the pressure of the sample
T
, the temperature of the sample
n
, the amount of substance in the sample
However, an astonishing experimental fact is that
these four quantities are not independent of one
another
. For instance, we cannot arbitrarily choose
to have a sample of 0.555 mol H
2
O in a volume of
100 cm
3
at 100 kPa and 500 K: it is found
experi
mentally
that the state simply does not exist. If we
select the amount, the volume, and the temperature,
then we ﬁnd that we have to accept a particular
pressure (in this case, close to 230 kPa). The same is
true of all substances, but the pressure in general
will be di
C
erent for each one. This experimental
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generalization is summarized by saying the substance
obeys an
equation of state
, an equation of the form
p
=
f
(
n
,
V
,
T
)
(1.1)
This expression tells us that the pressure is some
function of amount, volume, and temperature and
that if we know those three variables, then the
pressure can have only one value.
The equations of state of most substances are
not known, so in general we cannot write down an
explicit expression for the pressure in terms of the
other variables. However, certain equations of state
are known. In particular, the equation of state of a
lowpressure gas is known, and proves to be very
simple and very useful. This equation is used to
describe the behaviour of gases taking part in reac
tions, the behaviour of the atmosphere, as a starting
point for problems in chemical engineering, and
even in the description of the structures of stars.
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 Spring '08
 Loeblich
 Anatomy

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