Thermodynamics and the Flow of Heat through the Climate System - Climate Dynamics - page 89

5

THERMODYNAMICS AND THE
FLOW OF HEAT THROUGH
THE CLIMATE SYSTEM

Studying the thermodynamics of the atmosphere and oceans provides an under-
standing of how the solar radiation that fuels the climate system is converted
into other forms of energy within the system. The first law of thermodynamics ,
which states that energy can be converted from one form to another but never
created or destroyed, provides a foundation from which to study the flow of
heat through the climate system and to understand how that heating is related
to the circulation.

5.1 EQUATIONS OF STATE

State variables describe a thermodynamic system, and the relationship among
them is the equation of state . For the atmosphere, the state variables are pres-
sure ( p ), density (r), and temperature ( T ). The ideal gas law serves as an ac-
curate equation of state. We will use it in the form

p  r RT , (5.1)

where R is the gas constant for dry air, 287 J/(kg  K). According to Eq. 5.1, the
thermodynamic state of a parcel of air is fully determined if two of the three
state variables are known.
The equation of state for ocean water is more complicated. There are four
state variables, namely, pressure, water density, temperature, and salinity ( p ,
r w , T , and S ), and the relationship among them is not simple. A graphical
method is often used to determine the density of seawater.
Figure 5.1 is a T-S plot , which relates the density of seawater to temperature
and salinity. For the observed ranges of sea surface temperatures ( Fig. 2.15) ,
about 270 K (−3°C) to 303 K (30°C), and sea surface salinities, about 31-38
psu ( Fig. 2.19 ), seawater density ranges from roughly 1020 kg/m 3 to 1030 kg/
m 3 . The letter M indicates the approximate location of Mediterranean waters
on the T-S plot, and the letter A indicates Arctic waters.
The curvature of the isopycnals , or lines of constant density, in the T-S
plot indicates that the relationship between seawater density and temperature
is not linear. Figure 5.2a shows the dependence of the density of fresh water
( S  0) on temperature. As water is cooled from 20°C its density increases until