Geoscience Reference
In-Depth Information
the saltier (more dense) seawater blocks the transfer of heat between the ocean
and the atmosphere. With a sea ice barrier in place, atmospheric temperatures
up to 30°C cooler than sub-ice ocean temperatures have been observed.
5.2 THE FIRST LAW OF THERMODYNAMICS
The first law of thermodynamics is a statement of conservation of energy.
Heating (or cooling) of a parcel of air or water is balanced when the parcel
changes temperature, does work on the environment, or both. One form of the
thermodynamic equation is
dT
+=
d
c
p
dt
Q
,
(5.2)
v
dt
where
Q
is the rate at which heat is added to a parcel of air or water (W/m
2
),
called the
diabatic heating rate
. Radiative heating is one component of the
diabatic heating. Another form is sensible heating, due to conduction. Latent
heat releases when water condenses, and cooling due to evaporation, also con-
tribute to the diabatic heating rate.
The first term on the left in Eq. 5.2 represents a change in temperature of
the parcel if the volume is fixed, that is, if the parcel is constrained not to do
work on the environment by expanding. The constant
c
v
is the specific heat at
constant volume, essentially a proportionality constant that translates between
the diabatic heating rate (
Q
) and the rate of temperature change (
dT
/
dt
). The
second term on the left in Eq. 5.2 represents work done by the parcel in in-
creasing its volume in response to the addition of heat (a negative value means
that work is being done on the parcel by the environment when a parcel con-
tracts). Here, the symbol a denotes the specific volume, or the volume occupied
by a unit mass:
/
αρ
Another form of the thermodynamic equation is also useful for atmospheric
applications. Because changes in density are difficult to observe, the ideal gas
law is used obtain
1
/.
dp
dT
c
α−=,
Q
(5.3)
p
dt
dt
where
$
is the specific heat of air with pressure held constant.
c
1004 (
J/ kg K
)
p
(See exercise 5.1.)
Under
adiabatic conditions
, that is,
Q
0, Eq. 5.3 can be written as
dp
dT
R
R
dp
−= =
0
or
dT
c
ln
ln
,
(5.4)
T
c
p
p
p
where the ideal gas law (Eq. 5.1) was used to eliminate a. Integrating from the
surface (
T
S
,
p
S
) to some level in the atmosphere (
T
,
p
) gives
p
Rc
p
S
TT
p
fp
(5.5)
.
S
