Page 96 - Geosystems An Introduction to Physical Geography 4th Canadian Edition

60 part I The energy–Atmosphere system
geosystemsconnection
In this chapter, we found our place in the Universe and in relation to the milky Way galaxy, sun, other planets, and planetary satellites. We saw that, from the sun, the solar wind and electromag­ netic energy flow across space to earth; we looked at the equator­to­pole distribution of this radiant energy at the top of the atmosphere and at how it changes in a seasonal rhythm.
next we construct earth’s atmosphere and examine its composition, temperature, and functions. electromagnetic energy cascades toward earth’s surface through the layers of the atmosphere, where harmful wavelengths are filtered out. Also, we examine human impacts on the atmosphere: the depletion of the ozone layer, acid deposition, and variable atmospheric components, including human air pollution.
AQuantitativesoLUTIon Radiation and Temperature
radiation laws are the set of rules that summarise the way that matter interacts with the electromagnetic spectrum. We can think of radiation, energy, and temperature—the hotter a body, the more energy it radiates, and the shorter the mean wavelength of energy it radiates. two laws are particularly useful in an examina­ tion of energy.
these laws apply only to something known as a blackbody— a perfectly radiating surface. Most surfaces are not perfect radia­ tors, but the differences in radiation are not significant enough to discount the laws.
First is the Stefan­Boltzmann Law that gives the total amount of energy being emitted at all wavelengths by a blackbody,
E = sT4
where E is the energy measured in W·m−2, s is the Stefan­ Boltzmann constant (5.6705 × 10−8 W·m−2·K−4), and T is the temperature of the surface measured on the Kelvin scale. Kelvin is a scale of temperature that has an absolute zero: Zero Kelvin means there is no temperature. the measurement units are the same distance apart as on the Celsius scale—a relative tempera­ ture scale. to change from Kelvin to Celsius, use the following conversion:
k = °C + 273
Second is Wien’s Displacement Law that gives the wavelength of
the peak of the radiation distribution,
lMAX = Tc
where lMAX is the wavelength in μm that is the maximum
radiation at a given temperature, c is a constant (2898 μm·K),
and T is the surface temperature in K. the numerator is a constant usually measured in angstroms (one 10 billionth of a metre),
but can be measured in other units. In this example we use micrometres (μm).
to see how these laws are applied, consider normal room tem­ perature of 20°C. Convert this temperature to Kelvin by adding 273 to 20. room temperature in Kelvin is 293 K. Note that we do not use the degree symbol when measuring Kelvins. how much energy is being emitted by a surface at room temperature?
E = sT4
= (5.6705 × 10−8 W·m−2 · k−4) × (293 k)4
= (5.6705 × 10−8 W · m−2 · k−4) × 7.37 × 109 k4 = 417.9 W · m−2
= 418 W · m−2
What is the wavelength of the peak radiation emission?
60
l
MAX
= c T
= 2898 μm · k / 293 k = 9.89 μm
at room temperature, a surface emits 418 W·m−2 of thermal infra­ red energy at a peak wavelength of 9.89 μm.