Page 25 - Advanced Mine Ventilation

8 Advanced Mine Ventilation

1.3.1 Gas Laws Related to Air

Air just like all other gases follows many laws of physics that are essential to under-
stand its behavior. Only the most pertinent laws will be discussed here.

1.3.1.1 Boyle’s Law
The volume of air, V is inversely proportional to pressure, P at constant temperature, T.
For a given volume of gas changing from volume V 1 and pressure P 1 or to volume V 2
and pressure P 2 ,

P 1 V 1 ¼ P 2 V 2 (1.1)

1.3.1.2 Charles’ Law
The volume of air (gas) is directly proportional to the absolute temperature, T at con-
stant pressure.
Mathematically,

V 1 T 1
¼ (1.2)
V 2 T 2

Combining Eq. (1.1) and Eq. (1.2) we get the generalized gas law:

P 1 V 1 P 2 V 2
¼ ¼ R (1.3)
T 1 T 2
where R is the gas constant with a value of 53.35 ft-lb/lb mass R.

1.3.1.3 Dalton’s Law of Partial Pressure

It states that the pressure exerted by a mixture of gases is equal to the sum of separate
pressures that each gas would exert if it alone occupied the whole volume.
Mathematically,

PV ¼ V ðP 1 þ P 2 þ P 3 ; etcÞ (1.4)

where P is the pressure and P 1 ,P 2 ,P 3 , etc are partial pressures. In normal air, there are
only two gases, dry air and water vapor.

P ¼ P a þ P v

where P a ,P v are partial pressures of air and vapor.
An example:
Let us assume P (barometric pressure) is 30 inches of Hg
Partial pressure of vapor is 0.5 inch Hg