Compressibility
-
Compressibility
of any substance is the measure of its change in volume
under the action of external forces.
-
The normal compressive stress on
any fluid element at rest is known as hydrostatic pressure
p and arises as a result of innumerable molecular
collisions in the entire fluid.
-
The degree of compressibility of
a substance is characterized by the bulk modulus of
elasticity E defined as
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(2.3) |
Where Δ and
Δp are the changes in the volume and pressure respectively,
and is the initial volume. The negative sign (-sign)
is included to make E positive, since increase in pressure
would decrease the volume i.e for Δp>0
, Δ<0) in volume.
-
For a given mass
of a substance, the change in its volume and density satisfies
the relation
Dm = 0, D( ρ ) =
0
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(2.4) |
using |
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we get
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(2.5) |
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Values of E for liquids
are very high as compared with those of gases (except at
very high pressures). Therefore, liquids are usually termed
as incompressible fluids though, in fact, no substance is
theoretically incompressible with a value of E as
.
- For example, the bulk modulus of elasticity for water and air
at atmospheric pressure are approximately 2 x 106 kN/m 2 and 101 kN/m 2 respectively.
It indicates that air is about 20,000 times more compressible
than water. Hence water can be treated as incompressible.
- For gases another characteristic
parameter, known as compressibility K, is usually
defined , it is the reciprocal of E
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(2.6) |
K is often expressed in terms of specific volume
.
- For any gaseous substance, a change
in pressure is generally associated with a change in volume
and a change in temperature simultaneously. A functional
relationship between the pressure, volume and temperature
at any equilibrium state is known as thermodynamic equation
of state for the gas.
For an ideal gas,
the thermodynamic equation of state
is
given by
-
where T is the temperature
in absolute thermodynamic or gas temperature scale (which
are, in fact, identical), and R is known as the
characteristic gas constant, the value of which depends
upon a particular gas. However, this equation is also valid
for the real gases which are thermodynamically far from
their liquid phase. For air,
the value of R is 287 J/kg K.
- K and
E generally depend on the nature of process
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