4
1 Fundamental Concepts of Fluid Mechanics for Mine Ventilation
Therefore:
V α
nT
P
The concept of proportionality is resolved by introducing a constant, then:
V = R
nT
P
Or in its most common form (Eq. 1.5):
PV = n RT
(1.5)
where R is the universal constant of the molar, universal, or ideal gas constant. To
obtain its value, we can start from the previous expression. Since a mole of any gas
at 0 °C and one atmosphere pressure occupies 22.414 l, it can be deduced that:
R =
PV
nT
=
1 atm · 22.414 l
1 mol · 273 K
= 0.082
atm l
K mol
Alternatively:
R = 0.0831
bar l
K mol
= 8.314
kPa l
K mol
= 8.314
J
K mol
= 1.99
cal
K mol
1.2.3 Real Gases: van der Waals Equation
To better model the behaviour of real gases, van der Waals established a modification
of the previous equation. Specifically, it corrects the pressure (P) and volume (V )
terms (Eq. 1.6):
P +
an
2
V 2
(V − nb) = n RT
(1.6)
where
• a: Coefficient to account for intermolecular attractions, and
• b: Coefficient to account for the finite volume of the molecules.