GPHY 314 Quiz: Week 2

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29 Dec 2020
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WEEK 2: Earth’s Radiation Balance
Temperature and Energy
Energy: capacity to do work, represented in unit of joule (J)
o 1J ~amount of energy needed to lift 100g about 1m
o Power: rate at which energy flows, usually expressed in watts (W)
1W = 1J/sec, so 60-W bulb consumes 60J of energy ever second
A gallon is a quantity i.e. gallon of water -> Akin to joule
o Rate at which water flows through pipe measured in gallons per minute
Rate at which energy flows is the power, measured in watts (J per s)
Internal energy: how fast the atoms and molecules in the object are moving
o If water molecules moving slowly in one glass, it has less internal energy than water
moving on other glass
o In solid, movements of atoms are approx. fixed in space by intermolecular forces
But atoms can still move small distances around their fixed position
Faster atoms move about their fixed position, the more internal energy
Temperature: measure of internal energy of an object
o As internal energy increases and molecules of object speed up, temperature of object also
increases
o Kelvin scale: equal to temperature in degrees Celsius plus 273.15
Freezing temperate of 8°C is equal to 273.15K
Room temperature is ~22°C = 295K
Most temperatures found in Earth’s atmosphere between 200K and 300K,
average surface temperature ~288K
Preferred by physicists -> Temperature K proportional to internal energy
If temperature doubles from 200 to 400K, internal energy also doubles
0K is absolute zero -> Temperature at which molecules have zero internal energy
and cease moving; coldest possible temperature
Electromagnetic Radiation
Radiation: energy transported from Sun to Earth as electromagnetic waves i.e. visible light, x-
rays, radio wave, also known as electromagnetic radiation (EMR)
o Travels in bundles of energy called photons
o Can’t understand how much radiation is being absorbed by the earth without a good
understanding of the fundamental physics behind it
Everything emits radiation
o Emission: energy transferring out of an object
o Absorption: energy being taken in
EMR emitted at different wavelengths (distance between wave
crests) and frequencies (waves per time)
o Longer wavelength would have lower frequency, so
less waves make it through object in given period
o Photons with wavelengths between 0.3-0.8 microns
(millionth of a meter) can be seen with the human eye -> Refer to as visible photons
In visible range, different wavelengths appear as different colours
0.4 = blue, 0.6 = yellow, 0.8 = red
o Photons with wavelengths from 0.8-1000 microns are beyond the red end of the visible
spectrum, invisible to humans -> Refer to as infrared photons
Play important role in Earth’s climate and our everyday lives
o Photons with wavelengths just below human detection limit of 0.3 are beyond the violet
end of the visible spectrum -> Refer to as ultraviolet photons
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o Photons with wavelengths between 1000 microns and 0.3m are used in many familiar
applications i.e. cooking -> Refer to as microwaves
o Wavelengths longer than about 0.3m used in radio applications -> Refer to as
radiowaves
Wavelength determines photon’s physical properties
o Atmosphere is transparent to visible photons but not to infrared photons
Kirchhoff's law: absorptivity (a) for substance at given wavelength (λ) equal to its emissivity (ℇ)
o λ = aλ
o General principle -> A good absorber is a good emitter, and vice versa
Object that emits lota of radiation likely effective at absorbing lots of radiation
Blackbody Radiation
Everything around you is emitting photons all of the time
o Wavelength emitted is determined by object’s temperature
Blackbody: idealized body/planet that has no hinderance to its absorption/emission of energy
o Object or substance that emits at 100% efficiency for a given wavelength
o Not a representation of reality, but saying that if we were to assume no atmosphere or
perfection conditions, what should we expect?
Figure plots emissions spectra for blackbodies at three temperatures,
gray bars show wavelength range visible to humans
o An emissions spectrum shows the power carried away from an
object by the photons at each wavelength
o Photos emitted by 300K blackbody almost exclusively have
wavelengths greater than 4 microns
Outside range visible to humans, so all room-temperature
objects emitting photons but you can’t see them since
they’re outside the visible range
o Origin of blackbody -> At room temp, object appears black
because photons emitted are invisible to humans
o First figure also shows that the peak of emissions spectrum for
300K blackbody occurs near 10 micron
o Objects do not just emit photons at λmax -> Emit them over a
range of wavelengths around that
“Red hot” used to determine when a piece of metal has
reached an appropriate temperature, and necessity of
seeing a faint glow from an object is one reason
blacksmiths often work in dim, low-light conditions
o For 6000K object (bottom figure), most photos fall within visible
range i.e. Sun
Being able to see confers survival advantage so eyes have evolved to see this
range of wavelengths, maximally sensitive to light with wavelength near 0,5
microns, which is the λmax for a 6000K blackbody
What you see when you look at a room-temperature object are visible photons emitted by a hot
object that have bounced off the object
o Incandescent light bulb consists of glass envelope containing small filament made of
metal like tungsten
When bulb turned on, electricity flows through filament, heating to ~3000K
85% of photons emitted have wavelengths in infrared, too long for human eye to
detect -> Provide no lighting for humans so energy to produce them is essentially
wasted, making them inefficient as light sources
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o One way for bulb to produce a higher fraction of visible photons to run the filament at a
higher temperature, shifting distribution of emitted photos to shorter wavelengths,
making greater fraction of them visible to humans
Optimal temperature would be that of the Sun ~6000K, which provides best
overlap between blackbody emission and human visual range
But at this temperature, filament would immediately vaporize and bulb
would be destroyed
Conventional incandescent bulbs run at about as high a temperature as
they can be
Better way to obtain high efficiency lighting to change the technology
o Compact fluorescent light bulbs (CFL) and light emitting diode (LED) bulbs use different
technologies to emit most of the photons in the visible wavelength range
Net result is bulb at least x5 more efficient
Not only does wavelength of emission change with temp, but total power emitted also increases
o At every wavelength, warmer objects emit more power than cooler objects
Emission of Radiation
Three key radiation laws allow us to estimate the quantity and type of EMR emitted by blackbody
using just temperature
Wien’s Displacement Law
o Lets you calculate peak wavelength of energy emitted by blackbody using its temperature
o λmax = b / T
Peak emitted wavelength (unit: 10-7m) = constant (2.9 * 10-3m K) / absolute
temperature (K)
o Telling you where most of the energy is being emitted at
o Earth’s temperature about 288K, and you would expect peak wavelength to be in long-
wave portion
Much hotter planet i.e. Venus (~700K) wavelength much shorter
Much colder planet i.e. Pluto (~44K) wavelengths much longer
In terrestrial astrophysics i.e. finding planets suitable for life, can use
formula simply by rearranging it
Measure electromagnetic spectrum being emitted from star,
accurately detect peak wavelength, calculate temperature of
the surface of the terrestrial body
Stefan-Boltzmann Law
o Lets you calculate the total energy emitted by a blackbody using its temperature
o E = σT4
Energy per area per time (unit: J m-2 s-1) = Stefan-Boltzmann constant (5.67 * 10-
8 J s-1 K -4) * absolute temperature (K)
o Similar to Wien’s that they use absolute temperature
o Useful for other planets, as well as to sun and earth to find how much energy they’re
emitting
o Amount of energy radiated by an object increases with its temperature
Does an ice cube (0°C) emit radiation/energy? YES
Can an object of -272°C emit radiation? YES, since above absolute zero
What about our planet (288K)? YES, certainly
o Earth, Venus (higher temperature) giving off lots of energy, Pluto (colder
temperature) not giving off much energy
o By measuring amount of power emitted by object, astronomers use it to infer the
temperature of distant stars and planets, US military uses it to build sensors to
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