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Fluids
Ideal gas law
The properties of gases are in general well understood by
the relation
PV = NkT = nRT
The symbol P represents the absolute pressure,
V the volume,
T the temperature
and N is the number of particles in the gas.
k
represents the Boltzmann
constant
(1.38×10-23 JK-1).
n is the amount of gas expressed in
moles.
R
represents the ideal, or universal,
gas constant
(8.314 JK-1mol-1).
One has the following relations for
N,
n,
k,
R
and Avogadro's
number NA
(6.02×1023 mol-1).
N = n NA
and
R = k NA
Notice that the relation expressed by the ideal gas law
does not refer to the mass of the gas molecules.
At room temperature (T=293 K)
and at a standard pressure of
1 atm
(101325 Pa),
one finds for the volume of 1 mol
of a gas
V = nRT/P =
= (1 mol)×(8.314 JK-1mol-1)×(293 K)/(101325 Nm-2) =
0.024 m3
independent of the type of gas!
When at constant temperature T
the volume of a gas is changed from V1 to V2, then its pressure change, from
P1
to P2,
is determined by
P2 =
(V1/V2)
P1
(Boyle, 1662)
When at constant volume V
the temperature of a gas is changed from T1 to T2, then its pressure change, from
P1
to P2,
is determined by
P2 =
(T2/T1)
P1
(
Amontons, ~1700)
When at constant pressure p
the temperature of a gas is changed from T1 to T2, then its
volume change, from
V1
to V2,
is determined by
V2 =
(T1/T2)
V1
(
Charles, ~1780)
Boyle's law