## Hypsometric Relation

Heating
the atmosphere causes it to expand obtained by substitution of the hydrostatic equation (4) into
the equation of state.(1). This relation provides the basis of explaining
many, many things that synoptic meteorologists see on weather maps and charts.

Thickness of layer between two pressure surfaces is
directly related to the mean temperature of the layer.

Also, if we consider the thickness of a layer that is often of importance to
synoptic meteorologists, the layer approximately between the ground (1000 mb) and about 6 km (500 mb), the
Hypsometric Relation is

*where** k = R/g ln 2 and *∆Z is the thickness of the
layer between 1000 mb and 500 mb
and T_{v} is the Virtual Temperature, which
we will assume here is very close to the actual temperature.