EQUATION OF STATE
The equation of state is a general gas law for
finding pressure, temperature, or density of a dry gas.
Rather than using volume, this formula uses what is
called gas constant. A gas constant is a molecular
weight assigned to various gases. Actually, air does not
have a molecular weight because it is a mixture of gases
and there is no such thing as an air molecule. However,
it is possible to assign a so-called molecular weight to
dry air that makes the equation of state work. The gas
constant for air is 2,870 and for water vapor it is 1,800
when the pressure is expressed in millibars and the
density is expressed in metric tons per cubic meter. The
gas constant may be expressed differently depending
on the system of units used.
The following formula is an expression of the
equation of state:
P = rRT
P = pressure in millibars
r = density (Greek letter rho)
R = specific gas constant
T = temperature (absolute)
The key to this formula is the equal sign that
separates the two sides of the formula. This equal sign
means that the same value exists on both sides; both
sides of the equation are equal. If the left side of the
equation (pressure) changes, a corresponding change
must occur on the right side (either in the density or
temperature) to make the equation equal again.
Therefore, an increase of the total value on one side of
the Equation of State must be accompanied by an
increase of the total value on the other side. The same is
true of any decrease on either side.
NOTE: Since R is a constant it will always remain
unchanged in any computation.
The right side of the equation can balance out any
change in either density or temperature without having
a change on the left side (pressure). If, for example, an
increase in temperature is made on the right side, the
equation may be kept in balance by decreasing density.
This works for any value in the equation of state.
From this relationship, we can draw the following
A change in pressure, density (mass or
volume), or temperature requires a change in one or
both of the others.
With the temperature remaining constant, an
increase in density results in an increase in atmospheric
pressure. Conversely, a decrease in density results in a
decrease in pressure.
NOTE: Such a change could occur as a result of a
change in the water vapor content.
With an increase in temperature, the pressure
and/or density must change. In the free atmosphere, a
temperature increase frequently results in expansion of
the air to such an extent that the decrease in density
outweighs the temperature increase, and the pressure
actually decreases. Likewise, a temperature increase
allows an increase in moisture, which in turn decreases
density (mass of moist air is less than that of dry air).
temperature increase and almost invariably, the final
result is a decrease in pressure.
At first glance, it may appear that pressure
increases with an increase in temperature. Earlier,
however, it was noted that this occurs when volume (the
gas constant) remains constant. This condition would
be unlikely to occur in the free atmosphere because
temperature increases are associated with density
decreases, or vice versa. The entire concept of the
equation of state is based upon changes in density
rather than changes in temperature.
The hydrostatic equation incorporates pressure,
temperature, density, and altitude. These are the factors
that meteorologists must also deal with in any practical
application of gas laws. The hydrostatic equation,
therefore, has many applications in dealing with
atmospheric pressure and density in both the horizontal
and vertical planes. The hydrostatic equation itself will
be used in future units and lessons to explain pressure
gradients and vertical structure of pressure centers.
Since the equation deals with pressure, temperature,
and density, it is briefly discussed here.
hydrostatic equation and is used for either determining
the thickness between two pressure levels or reducing
the pressure observed at a given level to that at some
other level. The hypsometric formula states that the
difference in pressure between two points in the
atmosphere, one above the other, is equal to the weight
of the air column between the two points. There are two
variables that must be considered when applying this
formula to the atmosphere. They are temperature and