Page 60 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

34 2 Basic Properties of Gases

Substituting Eq. (2.8) into Eq. (2.27) we can get, with Eq. (2.25 below),
PV ¼ nRT ð2:33Þ

With q ¼ Nm=V, Eq. (2.33) becomes

qRT
P ¼ ð2:34Þ
M
This is the so called ideal gas law, where n is the mole amount of the gas, and
J J
R = the universal gas constant and R ¼ 8314 or 8:314 K:
kmol K mol
Example 2.1: Gas density calculation
Estimate dry air density at 0 °C and 1 atm using Eq. (2.34)

Solution
From Eq. (2.34) we have

PM 101; 325 PaðÞ 28:84ðkg=kmolÞ 3
q ¼ ¼ ¼ 1:29 kg=m
RT 8; 314J=ðkmol KÞ 273K

The universal ideal gas constant is related to the Boltzmann constant k as,

R ¼ kN A ð2:35Þ
As such, the ideal gas law can be rewritten in terms of the Boltzmann constants

PV ¼ nN A kT ¼ NkT ð2:36Þ

where N ¼ nN A Þ is the total number of molecules in the subject gas.
ð
Dalton’s law is an empirical law that was observed by John Dalton in 1801 and it
is related to the ideal gas law. It is important to air emission studies in that gases in
air emission engineering are often mixtures of multiple compounds.
Consider a mixture of gases, the mole number n of a gas mixture equals to the
sum of the mole numbers of all its components.

N
X
n ¼ n i ð2:37Þ
i¼1
and the mole fraction, denoted as y i , of any given species is

N
n i X
y i ¼ and y i ¼ 1 ð2:38Þ
n
i¼1