Met Office College - Course Notes
Physical Properties of Water
Contents
1. Phases of water
2. Latent heat
3. Water Vapour
3.1 Daltons law of partial pressures
3.2 Saturated and unsaturated vapour w.r.t. water
3.3 Saturated and unsaturated vapour w.r.t. ice
3.4 Using the eT diagram
4. Hydrological cycle
5. Summary
6. Further reading
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1. Phases of water
We shall be considering here the effects of water, in its various states, on
the atmosphere.
Within the normal range of atmospheric temperatures and pressures
water can, and does, exist in all three of its possible states, e.g. solid,
liquid and gas. Changes between these states have been given specific
names as shown in figure 1.
Sublimation
Melting
Ice
Evaporation
Water
Freezing
Condensation
Water
vapour
Deposition
Figure 1. Schematic diagram of phase changes for water
DEFINITIONS:
Condensation.
The formation of liquid from its vapour. In
meteorology, the formation of water from water
vapour.
Freezing.
A phase change from liquid to solid. It can only occur
at temperatures below 00C but liquid water can exist at
temperatures as low as -400C. Such water is known as
super-cooled water.
Melting.
A phase change from solid to liquid. This only occurs
at 00C. For this reason 00C is better referred to as the
melting point of water and not the freezing point.
Super-heated ice does not exist.
Evaporation.
A phase change from liquid to gas. It occurs from the
surface of the liquid (except in boiling water). The
energy input is very large. It is the main mechanism for
the transport of heat around the globe.
Sublimation.
The direct transition from solid to vapour without
going through an intermediate liquid phase. In physics
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Physical Properties Of Water
it also refers to a change from vapour to solid without
an intermediate liquid phase. In meteorology such a
change is usually referred to as deposition.
2. Latent heat
When a change of state occurs, heat energy is involved. If the change of
state is ice to water or water to vapour (gaseous), a higher state, then
heat MUST be supplied. If the change is to a lower state, then heat is
released by the substance. These changes of heat are known as LATENT
HEAT CHANGES.
Latent heat is the quantity of heat absorbed or emitted without a change
of temperature (or pressure) during a change of state of unit mass of
material.
There are three possible situations,
1.
Latent heat of fusion - solid to liquid
) or
2.
Latent heat of vaporisation - liquid to gas
) vice
3.
Latent heat of sublimation - solid to gas
) versa
The quantity of heat involved is enormous when compared to specific
heat capacity, see table 1 below.
Table 1. Values of latent and specific heats for water.
Specific heat of
Latent heat of
FORM
ENERGY REQUIRED
(Jkg-1K-1)
Ice
2,106
Water
4,187
Water Vapour at
constant pressure
Water Vapour at
constant volume
1,846
Melting
3.34 x 105
Evaporation
2.5 x 106
1,386
This tells us that 2 ½ million Joules of heat are required to boil away 1kg
of water. This is an enormous quantity of heat, if all of it was used to
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raise the temperature of the water the specific heat capacity would allow
it to warm by
2,500,000
or 597 Kelvin.
4218
These huge figures account for why over half of all the energy that
reaches the earth’s surface is NOT available to directly heat the
atmosphere. The energy is used to melt ice and evaporate water instead.
3. Water Vapour
Within the atmosphere water is held in all three of it’s states, gaseous,
liquid and solid. However, it is the behaviour of the vapour form that is
arguably the most important.
3.1
Dalton's law of partial pressures
Water vapour is a trace element within the atmosphere taken as a whole,
but local concentrations can be up to 4%. When an observation is made,
dry and wet bulb thermometers are read and dew-point, vapour
pressure and relative humidity calculated. Vapour pressure is that part
of the total atmospheric pressure which is exerted by water. Typical
values would range between 5 hPa and 15 hPa, or 0.5 to 1.5 % of the
total atmospheric pressure. The value obtained on the humidity slide
rule is the pressure water vapour would exert if it alone occupied the
same volume as the whole mixture. This statement is known as Dalton’s
law of partial pressures. Therefore the 5 hPa to 15 hPa of vapour
pressure is known as the partial pressure of water vapour, usually
denoted by the symbol, (e). Dalton’s law states:
The total pressure of a mixture of gases is the sum of the partial
pressures of each individual gas.
3.2
Saturated and unsaturated vapour w.r.t. water
Until now we have only considered unsaturated vapour. All air holds
some water vapour but usually less than the maximum it could hold.
When the amount of vapour in the air is below the maximum the
vapour is said to be unsaturated. The maximum amount is not fixed, it
varies depending on the temperature. The higher the temperature the
more water vapour the air could potentially hold. Figure 2 shows how
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much water vapour (in hPa) the air can hold as a maximum at different
temperatures. In particular, note that this is not a steady increase with
temperature but rises dramatically as the temperature increases. When
the maximum value is reached, for air at 00C the vapour pressure is
6.11mb, the vapour is then said to be saturated. Saturated vapour
pressure is denoted by the symbol, es.
Saturated
Vapour
Pressure (hPa)
1013.25
1 atmosphere
6.11
273
373
Temperature (K)
Figure 2. Saturated Vapour Pressure Curve with respect to water.
3.3
Saturated vapour w.r.t. ice
The foregoing has been with respect to (w.r.t.) water, in other words
over a water surface. Now let us consider two sealed boxes, one is halffilled with liquid water at a temperature of -100C and the other ice at the
same temperature. Both have totally dry air in the remainder of the box.
Initially there is no vapour in the air in both cases. However,
evaporation will take place immediately between the interface of water
and air, and sublimation between ice and air. Some of the more
energetic molecules will escape the water and ice surfaces and move into
the air. The energy the molecules need to escape the bonds of water is
less than the energy required to escape from the more rigid ice surface.
Consequently, more molecules escape from the water compared to the
ice even though the water and ice are at the same temperature. As time
goes by more molecules escape but some return to the water and ice.
When the amount escaping is the same as that returning an equilibrium
situation is achieved. The net amount of vapour in the air cannot
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Pressure
es hPa
Saturated vapour
pressure curve
w.r.t. water.
Super-saturated
vapour.
Unsaturated
vapour.
6.11
Saturated vapour
pressure curve
w.r.t. ice.
273
Temperature (K)
Figure 3. Saturated vapour pressure for water vapour with respect to water and ice surfaces.
increase further unless the temperature increases. The vapour is
therefore saturated. However, the amount of vapour in the air above the
water surface is greater than that over the ice because more molecules
escaped from the water surface by the time equilibrium was reached.
Therefore the saturated vapour pressure is greater over the water than
over the ice. This is a very important result, consequently we must
amend our saturated vapour pressure curve, shown in figure 2, at
temperatures below 00C to allow for the possibility of ice existing. The
new diagram is shown in figure 3, and is important when we consider
how precipitation is formed.
3.4 Using the e T diagram
The axes of the diagram in figure 3 are es and T, hence referenced as an
eT diagram. We can use an eT diagram to find the dew-point of the air
and, if the vapour pressure is below 6.11mb, the frost point. See figure 4.
Definitions:
Dew-point - The temperature at which the air (vapour) just becomes
saturated w.r.t. water, when cooled at constant pressure and liquid
water content.
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Frost-point - The temperature at which air just becomes saturated w.r.t.
an ice surface, when cooled at constant pressure and liquid water
Saturated vapour
pressure es hPa.
Saturated vapour
pressure curve
w.r.t. water
x
A
Saturated vapour
pressure curve
w.r.t. ice
Dew Point
Frost Point
Temperature (K)
Figure 4. How to find the dew point and frost point of a sample using the e T diagram.
content.
Referring to figure 4. When a parcel of unsaturated air at A, is cooled at
constant pressure and water content it meets the saturation vapour
pressure curve w.r.t. ice before that w.r.t. water, consequently the frost
point is always higher than the dew-point.
Vapour pressures have another common practical use, that of
calculating the relative humidity (RH).
RH = the ACTUAL amount of water vapour the air DOES hold = e
the MAXIMUM amount of water vapour the air CAN hold es
This is usually expressed as a percentage by multiplying by a hundred.
A thought worth pondering about the e T diagram is, what would
happen to vapour if its temperature falls below the saturation curve
w.r.t. water but above the saturation curve w.r.t. ice? Such an occurrence
happens frequently in temperate latitudes and is the basis of the theory
of droplet growth in clouds.
4. Hydrological cycle
So far we have mainly considered water vapour in the atmosphere but
water exists in all three forms and not exclusively in the atmosphere.
Globally averaged, about 1m of water evaporates from the surface of the
oceans a year! However, the amount of water, in all its forms, in the air
at any one time is no more than about 30mm. Each water molecule
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spends about a week in the atmosphere during which time it may have
moved a quarter of the way round the world! Water is also found as
surface water, lakes, rivers, oceans etc., and as ground water. To get an
idea of the relative amounts, if all the water in the world was averaged
over the surface area of the oceans they would amount to the figures
shown in table 2.
Table 2. Depth to which water in all its locations would fill an area the
size of the oceans.
Oceanic water
3800m
Land ice
76m
Ground water
19m
Lakes and rivers
4m
Atmospheric water
0.03m
The full cycle of events through which water passes in the
earth/atmosphere system is known as the hydrological cycle, see figure
Evaporation
Condensation in
clouds
Transpiration
from
vegetation
Precipitation
Evaporation
from seas
Evaporation
from soil
Soil percolation
Evaporation
from surface
water
Surface
run off
Ground flow
Ground
water
Figure 5. The Hydrological Cycle.
5.
From figure 5 it can be seen that the key to our weather is the movement
of water from the earth’s surface to the atmosphere by evaporation and
transpiration. Transpiration is the loss of water vapour from plants by
evaporation and diffusion from their stomata. On a good day a mature
oak tree can transpire 450 litres (100 gallons) of water. Meteorologists
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therefore need to now what affects the rate of evaporation. Since we
know that evaporation can only take place at a water (or ice) surface it
makes sense that to increase the rate of evaporation we could increase
the surface area of the water.
As saturated vapour (air) cannot accept any more vapour from the water
surface further evaporation can only take place if the air is dried or the
existing water vapour moved by a strengthening wind. If this doesn’t
occur the only other way to increase evaporation would be to raise the
temperature.
Such changes do occur on a day to day basis and affect the way we
describe the weather, such as muggy or fresh, cloudy or sunny, etc.
5. Summary
Three phases of water - solid, liquid and gas.
Latent heat is the quantity of heat absorbed or emitted without a change
of temperature during a change of state of unit mass of material.
Dalton’s law of partial pressure states that the total pressure of a
mixture of gases is equal to the sum of the partial pressures of each
individual gas.
eT diagram illustrates the variation of saturation vapour pressures with
temperature. From the diagram dew-point and frost-point can be
calculated. A very interesting area of the diagram exists where vapour
can be saturated with respect to ice but unsaturated with respect to
water.
Relative humidity is the amount of water vapour the air does hold
divided by the amount it could hold if the air were saturated. It is
usually expressed as a percentage.
Hydrological cycle - The cycle of events through which water passes in
the earth atmosphere system. It is usually displayed pictorially.
How to increase evaporation 1. Raise the temperature of air above the water
2. Increase the surface area of the water
3. Dry the air above the water
4. Strengthen the wind over the water
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6. Further reading
A course in Elementary Meteorology, Chapter 3 by Pedgley
The Meteorological Glossary by McIntosh
College Physics volume. 1, Chapters 8 & 9 by Gillam and King
Elements of Meteorology, Chapter 2 by Miller and Thompson
Essentials of Meteorology, Chapter 2.3 by McIntosh and Thom
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