Page 59 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

2.1 Gas Kinetics 33

where A ¼ the area of the wall on which force is exerted, and V ¼ the volume of
the container. Since Nm stands for the total mass of the gas, then the density of the
gas is

q ¼ Nm=V ð2:28Þ

Equation (2.27) can be further rewritten as

1 2
P ¼ qc rms ð2:29Þ
3
This formula demonstrates the relationship between a macroscopic property
(pressure) and a microscopic property (the root-mean-square speed). For example,
the pressure of a gas is due to collisions between molecules and the wall.

2.1.4 Density and Specific Volume of a Gas

In an engineering practice, we hardly use or even care about the exact number of
molecules in a volume. Rather we use the mole amount of gases, which is denoted
as n and

n ¼ N=N A ¼ Nm=M ð2:30Þ

Then, the gas density is described as

q ¼ nN A m=V ¼ nM=V ð2:31Þ

The equation allows us to estimate the density of a gas with known molar weight
by comparing with another gas with known density.
A term related to density is specific volume, which is the inverse of density
v ¼ 1=q ð2:32Þ

3
It has a unit of volume per mass, for example, m /kg.

2.1.5 Ideal Gas Law and Dalton’s Law

Air and typical gases of interest in air emissions are often considered as ideal gases.
The ideal gas law governs the relationship between the pressure P, the volume V,
and the temperature T of an ideal gas. It can be derived by continuing with the gas
molecular kinetics.