Page 63 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

2.1 Gas Kinetics 37

where m w = mass of water vapor in the given air volume and m w,s = mass of water
vapor required to saturate at this volume
Example 2.4: Vapor pressure
Relative humidity of air in a typical cool summer day in Canada is about 40 % and
it is known that the saturation pressure at 21°C is 25 mbar. What is the corre-
sponding vapor pressure in the air.
Solution
From Eq (2.43), we have

P w ¼ P sat RH ¼ 25:0 mbar 40 % ¼ 10 mbar

2.1.6 Kinetic Energy of Gas Molecules

Combining Eqs. (2.35) and (2.8) leads to the root-mean-square speed of an ideal gas
in terms of microscopic variables, molecular weight M and temperature T.

1=2 1=2
3RT 3RT

c rms ¼ ¼ ð2:45Þ
N a m M
This equation can be used to determine c rms of a known ideal gas at a certain
temperature. This formula shows that root-mean-square speed of a gas is propor-
tional to the square root of the temperature, so it increases with the increase in gas
temperature.
The molecular kinetic energy can be determined from root-mean-square speed.
Usually, it is quantified on a per mole base. The kinetic energy for 1 mol of ideal
gas can be calculated as,

1 2 3
e k ¼ N a mc rms ¼ RT ð2:46Þ
2 2
This equation shows that the kinetic energy of an ideal gas depends only on its
temperature. This implies that the molar kinetic energy of different gases is the same
at the same temperature.
Example 2.5: Gas kinetic energy
Compute root-mean-square speeds and the kinetic energy of 1 mol of the following
gases H 2 ,H 2 O vapor, air, and CO 2 at standard temperature of 293 K.