Page 296 - Fundamentals of Air Pollution

252 17. The Physics of the Atmosphere

These equations combine Boyle's law, which states that when temperature
is held constant the volume varies inversely with the pressure, and the
law of Guy-Lussac, which states that when pressure is held constant the
volume varies in proportion to the absolute temperature.

A. First Law of Thermodynamics
If a volume of air is held constant and a small amount of heat A/i is
added, the temperature of the air will increase by a small amount AT. This
can be expressed as

where c v is the specific heat at constant volume. In this case, all the heat
added is used to increase the internal energy of the volume affected by the
temperature. From the equation of state (Eq. 17-8), it can be seen that the
pressure will increase.
If, instead of being restricted, the volume of air considered is allowed to
remain at an equilibrium constant pressure and expand in volume, as well
as change temperature in response to the addition of heat, this can be
expressed as

By using the equation of state, the volume change can be replaced by a
corresponding pressure change:

where c p is the specific heat at constant pressure and equals c v + R d/ where
R d is the gas constant for dry air.

B. Adiabatic Processes
An adiabatic process is one with no loss or gain of heat to a volume of
air. If heat is supplied or withdrawn, the process is diabatic or nonadiabatic.
Near the earth's surface, where heat is exchanged between the earth and
the air, the processes are diabatic.
However, away from the surface, processes frequently are adiabatic. For
example, if a volume (parcel) of air is forced upward over a ridge, the
upward-moving air will encounter decreased atmospheric pressure and
will expand and cool. If the air is not saturated with water vapor, the
process is called dry adiabatic. Since no heat is added or subtracted, &h in
Eq. (17-13) can be set equal to zero, and introducing the hydrostatic equation

and combining equations results in