Lecture 7. Water and water vapor in the atmosphere 30 Sep 2010
•Review of buoyancy, with an unusual demonstration of Archimedes principle.
•Water is a polar molecule that forms hydrogen bonds. Consequently water is a
structured liquid (and solid!). Water has a very high latent heat for evaporation and
fusion, due to the forces between molecules associated with hydrogen bonds (2.5 x
106 J/kg). Ice is highly ordered, less dense than liquid water (very unusual), and has
significant latent heat of fusion (0.34 x 106 J/kg).
•Evaporation and condensation are dynamic processes always taking place at the
liquid-air interface. The rate of evaporation increases with temperature. When the
rate of evaporation equals the rate of condensation, the air and water are in
equilibrium, and the air is said to be saturated with water vapor. The relationship
between water vapor pressure and temperature is the Clausius-Clapeyron equation.
Psat = A exp [B( 1/273.15 – 1/T)] B= 5308K. A=6.11 mbar=vapor press. 0C.
•Vapor pressure increases sharply with temperature, due to the large latent heat.
Water vapor content of air may be reported as partial pressure, relative humidity, dew
point or frost point, or specific humidity. In general water vapor content is smaller
than Psat, never significantly greater.
•Discuss the observed distribution of temperature in the atmosphere.
•When an air parcel moves up or down, its pressure changes according to the
barometric law. Forces act on the parcel and change its size, meaning that work is
done on/by the parcel. Work done on an air parcel by atmosphere, or by the parcel
on the atmosphere, is related to change in the temperature of the air parcel.
H
O
(—)
+
H
+
(—)
One side of the water molecule has a negative electric charge, balanced by a positive
charge on the other side. Water is a "polar" molecule.
The positive side of each water molecule interacts strongly with the negative side of
other water molecules. Water makes "hydrogen bonds", in ice, liquid, and vapor.
A great deal of energy is needed to pull a water molecule out of the liquid, because of
the strong hydrogen bonds. 2.26 × 106 J/kg needed to evaporate water.
For comparison: 4.2 × 103 J/kg needed to raise the temperature of water by 1 K (1 C).
The amount of energy needed to evaporate 1 kg of water is called the
latent heat of vaporization.
It is much larger for water than for most other liquids (due to hydrogen bonding).
Evaporation and condensation
Molecules are constantly evaporating from the
surface of a liquid. Molecules in the gas above the
liquid are constantly hitting the surface and
condensing. The molecules that evaporate take
energy from the liquid; the molecules that condense
add energy.
When a liquid is placed into a closed container, it will
eventually reach a steady state where molecules
evaporate from the surface and condense at exactly
the same rate. Even though the molecules are
constantly evaporating and condensing, there is no
net transfer of molecules, or of energy.
Lecture 7. Water and water vapor in the atmosphere
•Review of buoyancy, with an unusual demonstration of Archimedes principle.
•Water is a polar molecule that forms hydrogen bonds. Consequently water is a
structured liquid (and solid!).
•Evaporation and condensation are dynamic processes always taking place at the
liquid-air interface. The rate of evaporation increases with temperature.
•When the rate of evaporation equals the rate of condensation, the air and water are
in equilibrium, and the air is said to be saturated with water vapor. The relationship
between water vapor pressure and temperature is the Clausius-Clapeyron equation.
•Water has a very high latent heat for evaporation and fusion, due to the forces
between molecules associated with hydrogen bonds (2.5 x 106 J/kg). Thus the
Clausius-Clapeyron equation shows a steep increase in vapor pressure with
temperature:
Psat = A exp [B( 1/273.15 – 1/T)] B= 5308K. A=6.11 mbar=water vapor press. at 0C.
•Ice is highly ordered, less dense than liquid water (very unusual), and has significant
latent heat of fusion (0.34 x 106 J/kg).
•Water vapor content of air may be reported as partial pressure, relative humidity,
dew point or frost point, or specific humidity. In general water vapor content is
smaller than Psat, never greater.
Vapor Pressure
of Water
Psat = A exp [B( 1/273.15 – 1/T)] A=6.11
mbar, B= 5308K. A=water vapor pressure at
0C.
The pressure of
H2O vapor in
equilibrium with
liquid water.
ClausiusClapeyron
relation. Water
vapor pressure
versus T.
2253 kJ required for latent
heat of evaporation– 1kg
335 kJ required
for latent heat
of fusion
6
Lecture 7. Water and water vapor in the atmosphere
•Review of buoyancy, with an unusual demonstration of Archimedes principle.
•Water is a polar molecule that forms hydrogen bonds. Consequently water is a
structured liquid (and solid!).
•Evaporation and condensation are dynamic processes always taking place at the
liquid-air interface. The rate of evaporation increases with temperature.
•When the rate of evaporation equals the rate of condensation, the air and water are
in equilibrium, and the air is said to be saturated with water vapor. The relationship
between water vapor pressure and temperature is the Clausius-Clapeyron equation.
•Water has a very high latent heat for evaporation and fusion, due to the forces
between molecules associated with hydrogen bonds (2.5 x 106 J/kg). Thus the
Clausius-Clapeyron equation shows a steep increase in vapor pressure with
temperature:
Psat = A exp [B( 1/273.15 – 1/T)] B= 5308K. A=6.11 mbar=water vapor press. at 0C.
•Ice is highly ordered, less dense than liquid water (very unusual), and has significant
latent heat of fusion (0.34 x 106 J/kg).
•Water vapor content of air may be reported as partial pressure, relative humidity,
dew point or frost point, or specific humidity. In general water vapor content is
smaller than Psat, never greater.
Vapor pressures of water
and ice at atmospheric
temperatures.
Measuring the water vapor
content of the
atmosphere.
Relative humidity—air has a
given amount of water vapor
(partial pressure P, mb). In
general it will have less
water vapor than in
equilibrium with liquid at the
same T.
Relative Humidity:
Pwater/Psaturated (x 100, %)
Dew point: Temperature to
which you would have to
cool the air to have 100%
humidity (liquid
condensation starts).
Frost point: ice condenses.
Specific Humidity: kg of
H2O / kg of air
NOTE: "supercooling of droplets"
Why does a person's breath become visible (or not) when
mixing with outside air?
Lecture 7. Water and water vapor in the atmosphere
•Review of buoyancy, with an unusual demonstration of Archimedes principle.
•Water is a polar molecule that forms hydrogen bonds. Consequently water is a
structured liquid (and solid!).
•Evaporation and condensation are dynamic processes always taking place at the
liquid-air interface. The rate of evaporation increases with temperature.
•When the rate of evaporation equals the rate of condensation, the air and water are
in equilibrium, and the air is said to be saturated with water vapor. The relationship
between water vapor pressure and temperature is the Clausius-Clapeyron equation.
•Water has a very high latent heat for evaporation and fusion, due to the forces
between molecules associated with hydrogen bonds (2.5 x 106 J/kg). Thus the
Clausius-Clapeyron equation shows a steep increase in vapor pressure with
temperature:
Psat = A exp [B( 1/273.15 – 1/T)] B= 5308K. A=6.11 mbar=water vapor press. at 0C.
•Ice is highly ordered, less dense than liquid water (very unusual), and has significant
latent heat of fusion (0.34 x 106 J/kg).
•Water vapor content of air may be reported as partial pressure, relative humidity,
dew point or frost point, or specific humidity. In general water vapor content is
smaller than Psat, never greater.
•Introduce atmospheric temperature regions.
50
60
The change in temperature with
altitude in the atmosphere. The
example is from 30 degrees north
latitude in summer.
Altitude (km)
40
30
Why does T decrease
with altitude?
0
10
20
(There are two physical processes
at work: mechanical and radiative.
The next lecture material focuses
on the mechanical aspects.ˆ)
200
220
240
260
T( K)
280
300
The concept of an air parcel
1) It's a distinct 'block' of air in an environment of … air; we often assume it has
volume of 1 m3. It has to be small enough so that it has uniform properties (T, P, etc).
It’s a fictional entity that helps us to think through a physical process.
2) We can follow it (as if it were colored with dye) and it stays together (the same
molecules are inside at the end of a process as there originally).
3) At the beginning of any of thought exercise, it has the same characteristics as its
surrounding environment.
4) The parcel can change with time, by moving, emitting or absorbing heat radiation,
etc --usually in a way we can describe with equations.
5) The environment of the parcel can change too. The parcel changes as a parcel
NOT necessarily with the environment.
Question: Where does the energy come from for an
air parcel to do this work on the atmosphere?
Change of atmospheric temperature with altitude (  pressure )
Atmospheric pressure vs altitude follows the barometric law, P=- gz .
Let's think of an ideal case where the buoyancy forces and the weight of an air parcel
are perfectly balanced at every altitude, and we neither add or remove heat as the
parcel moves. Because an air parcel expands as pressure is lowered, it must do work
on the atmosphere as it moves up. The only source of energy is the motion of the
molecules, and therefore the air parcel must get colder as it moves up.
Two steps are needed to understand how an air parcel that moves up or down
changes it temperature.
Step 1. Figure out the exchanges of energy between the air parcel and the
environment as the parcel changes its pressure, using the definition of heat capacity
and Boyle's law.
Step 2. Relate this energy balance to the change in altitude, using the barometric
law.
Boyle's Law: P1V1 = P2V2
How can we use Boyle's Law to
determine the change in V when P
changes, for a parcel of air (at constant
temperature)? Boyles Law:
P2V2 = P1V1 + P1V + V1P + PV
= P1V1
Boyles law
P1V1
V
(P1 + P1)( V1 + V1) =
P2V2
P1V = — V1P, or P/V = — P1/V1
P
P1+P1 = P2 ; V1 + V1 = V2
This is an example of how we can understand the relationship between two properties
of air (or any gas), when both change together, by dividing the process into very small
steps where one changes while the other is held constant, then hold the first constant
and change the one initially held fixed.
V/V1 = ─ P/P1
How do we get energy out of molecular motion:
Heat capacity or Specific heat of a substance
The specific heat (Cp) of a substance is defined as the energy needed to raise the
temperature of 1 kg by 1o K (the "p" denotes that the pressure is held constant). This
energy goes into the thermal motions of the atoms and molecules (think of the "golf-ball
atmosphere" demo). The specific heat is a quantity we can measure for any gas. It tells
us how much energy we extract from the motion of the molecules to lower the
temperature of 1 kg by 1o K.
The energy obtained by lowering T is the negative of this amount:
[ Energy that must be added to a parcel to change T by T ]
P
= m cp T
h
[ Energy obtained (total) by lowering T by T ] = — m cp T.
Work done against (or by) atmospheric pressure to change
the pressure of an air parcel by P is given by P V.
( e.g., for the cylinder at the right, Work = h F = P A h = P V )
- m cp T = P V
(basic energy balance)
P
Piston
with top
area A,
volume
Ah
h
- mcp T = P V
(basic energy balance)
VP = - P V
(Boyle’s law) =>> - mcp T = - VP
P = - g  Z
(Barometric law) =>>- mcp T = (V g Z
 V = m = mass of parcel
We see that for an air parcel moving vertically in a hydrostatic atmosphere (barometric
law applies),
- cp T = g Z
T / z = -g/cp = - 9.8 oK/km
This change in temperature with altitude is called the "adiabatic lapse rate".
cp = 1005 J/kg/K; g = 9.8 m s-2 =>> - g / cp = — 9.8 x 10-3 K/m or — 9.8 K/km.
Lecture 7. Water and water vapor in the atmosphere 30 Sep 2010
•Review of buoyancy, with an unusual demonstration of Archimedes principle.
•Water is a polar molecule that forms hydrogen bonds. Consequently water is a
structured liquid (and solid!). Water has a very high latent heat for evaporation and
fusion, due to the forces between molecules associated with hydrogen bonds (2.5 x
106 J/kg). Ice is highly ordered, less dense than liquid water (very unusual), and has
significant latent heat of fusion (0.34 x 106 J/kg).
•Evaporation and condensation are dynamic processes always taking place at the
liquid-air interface. The rate of evaporation increases with temperature. When the
rate of evaporation equals the rate of condensation, the air and water are in
equilibrium, and the air is said to be saturated with water vapor. The relationship
between water vapor pressure and temperature is the Clausius-Clapeyron equation.
Psat = A exp [B( 1/273.15 – 1/T)] B= 5308K. A=6.11 mbar=vapor press. 0oC.
•Vapor pressure increases sharply with temperature, due to the large latent heat.
Water vapor content of air may be reported as partial pressure, relative humidity, dew
point or frost point, or specific humidity. In general water vapor content is smaller
than Psat, never significantly greater.
•Discuss the observed distribution of temperature in the atmosphere.
•When an air parcel moves up or down, its pressure changes according to the
barometric law. Forces act on the parcel and change its size, meaning that work is
done on/by the parcel. Work done on an air parcel by atmosphere, or by the parcel
on the atmosphere, is related to change in the temperature of the air parcel.
Global Sea Surface Temperatures February 2002
Global Sea Surface Temperature Anomalies, December 2001
10 Feb 2002
GOES ir image
10 Feb 2002
GOES ir image
/www.cira.colostate.edu/Special/CurrWx/g8full40.asp
Feb 2003
Global Sea Surface Temperature Anomalies, Dec. 2001, Jan 2003
12-2001
La Niña
01-2003
El Niño