Energy is defined as the capacity to do work on some form of matter.
The fundamental unit of energy is the Joule, which can be thought of
as the amount of energy exchanged during some change of state, such as a change
in temperature, or a change of elevation, or a chemical reaction. An important
related concept is that of power, which can be thought of as the rate
of energy delivery. The unit of power is the Watt (1 Watt = 1 Joule per
second). Thus, if a power of 1 Watt is sustained for 10 seconds, it can do 10
Joules of work. Similarly, if a power of 10 Watts is sustained for one second,
it can do10 Joules of work.
Energy cannot be destroyed: in the course of doing work, it is transformed
from one form into another. There are numerous forms of energy, including:
The transformation of energy can be observed around us constantly. One example
is the use of a gas stove to heat a pan of water. The gas is a fossil
fuel, that is, it consists of hydrocarbons originally synthesised by plants.
The plants used radiant energy from the sun to build complex molecules
from simple ones (mainly CO2 and water). Thus, they converted solar
energy to chemical energy (locked up in the bonds between the atoms making
up molecules), and additional chemical changes occurred during long burial underground.
Burning the fuel converts the chemical energy into heat (a manifestation
of random motions of molecules or molecular kinetic energy) and radiant
energy (infrared and a little bit of visible). The heat is conducted into
the pan and the water. The increase in the temperature of the water is a manifestation
of the increase in the molecular kinetic energy of the water. Some of the kinetic
energy, however, is not manifest as a change in temperature, but a change
in state: water is converted from liquid into gas, i.e. water vapour. The
energy involved in that transition is called latent heat. The water vapour
released from the pan of water rises: it is gaining gravitational potential
energy. Think about this the next time you brew a pot of coffee.
In the atmosphere, the most important forms of energy are radiation, kinetic
and potential energy. In the following sections we will examine some examples,
and the processes of transfer from one form to another.
The sun emits radiation at a range of wavelengths, known as the solar spectrum.
The peak of the solar spectrum is in the visible wavelengths (0.4 - 0.7 mm)
(mm or Greek mu m stands for micrometres; 1 mm
= 1 millionth of a metre, or 10-6 m). The shorter end of the visible
(0.4 mm) is violet light, whereas the longer
end (0.7 mm) is red. The solar spectrum also contains
significant near infrared (IR: 0.7 - c. 2.0 mm) and
ultraviolet (UV: c. 0.1 - 0.4 mm) when it arrives
at the top of the atmosphere. Collectively, the solar radiation is commonly
known as shortwave radiation. Some of this, especially the UV, is absorbed
before it reaches the lower atmosphere. The solar power at the top of the atmosphere
is c. 1370 W m-2 (Watts per square metre); or 1370 J sec-1
m-2 (Joules per second per square metre). This is known as the solar
constant, although it is not actually constant, but varies on a range of
cycles, such as the 11 year sunspot cycle.
Scattering by clear air is known as Rayleigh scatter. Molecules of air are most efficient at scattering radiation at the blue end of the spectrum: this is why the sky appears blue. The corollary of this is visible at dawn or dusk: a reddening of the atmosphere viewed towards the low sun. The low sky appears red because the shorter wavelength (blue) light has been scattered out of the line of sight.
Significant scattering also occurs off cloud droplets: this is known as Mie scatter. This is equally effective for all wavelengths, so clouds appear white. Another example of Mie scattering is whiteout conditions in blizzards.
The amount of reflection or backscatter that occurs from surfaces is measured
by the albedo. Albedo is defined as the percentage or proportion of incident
radiation that is reflected back off a surface. The average albedo of the Earth
= 0.3 or 30%. However, albedo varies greatly between different surfaces: snow
has a high albedo, whereas coal dust has a low albedo. Albedo is wavelength-dependent,
which is why objects appear different colours. Leaves reflect mostly green light,
absorbing other wavelengths to fuel photosynthesis.
lmax =2897/T
where T is temperature in degrees Kelvin (0o C = 273o
K)
l is the Greek letter lambda, and is used to denote
wavelength in mm.
Example
The surface temperature of the Sun = 5800o K, so from Wien's Law,
2897/5800 = 0.499
therefore, the peak in the solar spectrum is c. 0.5 micrometres (green light).
In contrast, for typical Earth surface temperature = 283o K (10o C), Wien's Law gives,
2897/283 = 10.24
Therefore, the peak in terrestrial spectrum is about 10 micrometres (infrared).
Thus, emitted radiation from the Earth is predominantly infrared: this is known as longwave radiation. The power of emitted radiation is also dependent on body temperature. This is given by the Stephan-Bolzmann Law:
E* = s T4
where E* is the power of the emitted radiation (W m-2),
s is a constant - the Stephan-Bolzmann constant =
5.67 x 10-8, and
T4 is the fourth power of the body temperature in degress Kelvin.
Strictly, this law applies to a perfect radiator, known as a blackbody. For real surfaces, we need to modify this by taking into account the emissivity, e, of the substance, or the fraction of the blackbody value that it actually does emit. For many Earth-surface materials, e = 0.90 - 0.98.
For sandstone at a temperature of 283o K (e = 0.98),
E* = 0.98 x 5.67 x 10-8 x 2834
= 357 W m-2
To put this into perspective, this power is about the same as that of visible light on a dull, cloudy day.
Together, Wien's law and the Stephan-Bolzmann law tell us that the Earth's emitted radiation is in the infra-red and of fairly low power. If we could see in the infrared, the Earth would glow gently in the dark. Terrestrial longwave radiation is strongly absorbed by the atmosphere, so the terrestrial radiation is more important in heating the atmosphere than direct solar (shortwave) radiation. The amount of radiation that passes through the atmosphere is measured by atmospheric transmissivity, Ta, which varies from gas to gas. Graphs of the wavelength of radiation leaving the earth's atmosphere displays a series of absorption bands attributable to different atmospheric constituents. Water (vapour and clouds) is exceptionally important in closing the 'atmospheric window'. We know this from experience: clear nights are much colder than cloudy nights because more longwave radiation can escape out into space.
In summary, incoming shortwave warms ground and water surfaces, which emit
longwave radiation, some of which is absorbed by the atmosphere - especially
cloudy atmospheres - thus heating the air.
Molecular kinetic energy is called sensible heat, because it can be felt by the senses. Sensible heat can be transferred from one place to another by various processes. First, conduction involves direct exchange of momentum between molecules, as in an iron bar heated at one end, or a pan of water sitting on a gas stove. Air, however, is a very poor conductor of heat. Much more important in the atmosphere is the bulk transfer of heat by moving air known as advection (where motions are mainly horizontal) or convection (where motions are predominantly vertical). Thus air heated at ground level can be lofted to higher levels by convection (the uplift of buoyant air masses), or by turbulent winds blowing over the surface. This latter process is known as turbulent heat transfer. One example of turbulent heat transfer is the wind chill effect: in still air, naked skin can be exposed even at quite low temperatures, because air heated by our bodies remains close to the skin, thus minimising further heat losses. However, in windy conditions, this warm boundary layer can be stripped away and constantly replaced by cold air, thus advecting heat away from the body. For the same reasons, winds are very important in transferring heat to and from ground surfaces.
The molecular kinetic energy of a substance is not simply a function of its temperature: it also depends on its state (i.e. solid, liquid or gas). For a given temperature, the liquid form substance will have a higher molecular kinetic energy than the solid form; similarly for a constant temperature the gaseous form substance will have a higher molecular kinetic energy than the liquid form. This is because energy is required to break free of inter-molecular bonds. It follows that energy is required to transfer a substance from solid to liquid, or liquid to gas, and that energy will be released during the transfer from gas to liquid or liquid to gas. This energy is known as latent heat ('latent' because it is 'hidden' within the substance). In short, latent heat is released or absorbed when the material changes state.
Latent heat plays a huge role in the atmosphere during changes of state of
water. The amount of heat required to melt ice (latent heat of melting)
= 334 J g-1. That is, 334 Joules are required to melt 1 gram
of ice. The same amount of energy (the latent heat of fusion) is released when
water refreezes to ice. Similarly, the energy required to evaporate water
= 2,500 J g-1, and this is released again upon condensation.
Sublimation, or the direct transition of ice to vapour, requires 2,834
J g-1, i.e. the sum of the latent heats of melting and evaporation.
The transfer of latent heat very important in the atmosphere, and contributes
a huge amount to global energy transfer.
An example of energy at work is the melting of glacier ice. We can use the information
given in this lecture to calculate how much ice will be melted from a glacier
surface under given climatic inputs. We know how much energy is rquired to melt
ice: 334 Joules for every gram. We also know that I Joule = 1 Watt sustained
for 1 second. What we need is the amount of energy absorbed by the ice in a
given time period. A simple form of the energy balance equation for an ice surface
is:
M = S + L + H
M is the energy available to melt ice
S is the absorbed shortwave radiation
L is the net longwave radiation (incoming minus outgoing)
H is the sensible heat transfer.
S and L can be measured directly using radiometers sensitive to the relevant wavelengths, while H can be calculated from measurements of ice surface temperature, air temperature, windspeed, and constants determined by the roughness of the surface. Fluxes down towards the surface are positive, and fluxes away from the surface are negative.
For Ngozumpa Glacier in the Mount Everest region, the following data were obtained as part of a study of ice melting:
S(incoming) = 1064 W m-2
S (outgoing) = - 94 W m-2
L (incoming - outgoing) = -91 W m-2
H = 10 W m-2
The net shortwave radiation is therefore 970 W m-2 (this means the albedo is 0.088: this is typical of dirty, very wet ice surfaces). The negative value of L means that more longwave energy was radiated off the surface than was received. The energy balance equation is therefore:
M = 970 - 91 + 10 = 808 W m-2
If this value is sustained for one hour (60 seconds x 60 minutes), the total work done will be:
808 x 60 x 60 = 2,908,800 Joules.
We know that 334 Joules are needed to melt 1 gram of ice, so
2,908,800 / 334 = 8709
so the available energy can melt 8709 grams of ice in one hour. It is useful to convert this into a thickness of ice melted. 1 cubic metre of ice has a mass of about 900 kg or 900,000 grams. If the ice block has an upper surface area of 1 m2, then a 1mm thickness of ice has a mass of 900 grams.
8709 / 900 = 9.68
so, in one hour, 9.68 mm of ice is melted.
This agrees very well with measured values. Full energy balance studies do
similar calculations for long time periods, using meteorological data obtained
from automatic weather stations, and are used to understand the response of
glaciers to climatic change. Similar energy balance models can be used to calculate
evaporation, the likelihood of ice forming on roads over night, and many other
applications.