Why do we think space is so cold?

• The upper atmosphere (ionosphere) and the space beyond (heliosphere) are hot plasmas, not cold and empty
• This unit will define heat and temperature, highlight their differences, and discuss the kinetic theory of gases

• Heat refers to an energy transfer from one object to another, due to a temperature difference
• Objects are in thermal contact if energy can transfer from one to the other
• Thermal equilibrium occurs when the energy transfer ceases and the two objects reach the same temperature

• Many properties of matter depend on temperature
• Temperature is usually considered a measure of how “hot” or “cold” an object is
• Scientists need a reliable and repeatable instrument to measure temperature – the thermometer!

• Establish a scale based on a measurable physical property of matter, such as length, volume, or electrical resistance
• Place thermometer in contact with object to be measured
• When thermometer is in thermal equilibrium with object – you’ve found the object’s temperature

• Galilean thermometer uses expansion of air in glass bulbs
• Students should be familiar with alcohol-based lab thermometer
(replaced Mercury-in-glass thermometer, invented by
Daniel Fahrenheit)
• Many home thermostats use expansion of bimetallic strip
Image from Hustvedt - Wikipedia

• Early thermometers had no scale
• Establishing a temperature scale requires one or more reference points
• Physical properties such as boiling or freezing point make an excellent reference

• Fahrenheit and Celsius scales were originally based on the freezing and boiling points of water
Scale
Fahrenheit
Celsius
Kelvin
Freezing Point Boiling Point
32 ºF
0 ºC
212
100
ºF
ºC
273.15 K 373.15 K

• Two points define the scale
• The first point is absolute zero
– No temperature can go below this point
– Defined as 0 K
• The second is the triple point of water
– This is the temperature at which H
2
0 can exist as a solid, liquid, and gas
– Defined as 273.16 K (+0.01 °C)
• Triple point pressure P = 6.03 x 10 -3 atm

• Many equations have a temperature term
– you don’t want to be dividing by zero!
• Does an object at 80 ºF have twice the energy as it did at 40 ºF? What about comparing 20 ºF = 2 x -10 ºF?
– No!!! The Kelvin temperature is directly proportional to the molecular energy, so it would make sense to say that something at
400 K has twice the internal energy as 200 K

• It is traditional to not use the degree symbol ( º) with the Kelvin scale
• A change of 1 kelvin is equivalent to a change of 1 degree Celsius
• Notice that the SI unit, when written out, uses a lower-case k, but the symbol is K

• Lord Kelvin was a Scottish scientist (born in Belfast) named William Thomson who contributed to many areas of science
• Your students will never forget to use kelvins if you shout this cheer:
Kelvin! Kelvin! He’s the best!
He surpasses all the rest!
Go-ooooo Kelvin!

• Converting between the different scales is a simple algebra problem
T
K
= T
C
ΔT
C
+ 273.15
= ΔT
K
T
F
= 9/5 T
C
+ 32
T
C
= 5/9 (T
F
ΔT
C
– 32)
= 5/9 ΔT
F

• From Planck’s blackbody law, objects will
“glow” in visible spectrum if they have sufficient internal temperature
• Objects can be “red hot” or “white hot”
– (why not “green hot”? – see inquiry)
• The spectral output of any object can be equated to a specific temperature

Temperature
1700 K
1850 K
2700 - 3300 K
4100 K
5000 K
5500 - 6000 K
6500 K
Source
Match flame
Candle flame
Incandescent light bulb
Moonlight
Horizon daylight
Typical daylight
Overcast daylight

• Walk into any hardware store to buy the new compact fluorescent light, and you are faced with an array of choices
• Names may vary over the spectrum of choices (pun intended)
Image courtesy US Environmental Protection Agency/Department of Energy

• Photographic film (or the CCD in a digital camera) is “balanced” to a certain color temperature
• In order to get true (accurate) color representation, the light source color temperature must match the film/CCD color temperature

• If the film/CCD and the scene lighting are not the same color temperature, your picture may appear bluish (cool) or slightly orange (warm)
– Cool and warm are human perceptions. The color temp of the scene lighting is actually higher (hotter) than film/CCD for cool pictures and lower (cooler) for warm pictures!
– Hotter light source will have more spectral content in the higher frequencies (blue end)
– Cooler light sources will have more spectral content in the lower frequencies (red end), less in higher frequencies

• For gases, temperature is proportional to the kinetic energy of the molecules
• Since KE = ½ mv 2 , the faster the molecules move, the higher the temperature
• Twice the KE yields twice the temperature

• A gas does not have a fixed volume
• Will expand to fill container
• Collection of randomly moving particles
• All of the electrons are bound to nuclei, no freely moving charges

• In chemistry, PV = nRT
– P is pressure (atm)
– V is volume (liters)
– n is the number of moles
– T is temperature (kelvins)
– R is the Universal Gas Constant
• 0.0821 L ·atm/mole·K

• In Physics, PV = Nk
B
T
– P is pressure (in pascals)
– V is volume (in meters-cubed)
– N is the number of molecules
• (N = n ·N
A
, where N
A is Avogadro’s Number)
– T is the temperature (kelvins)
– k
B is Boltzmann’s constant
• 1.38 x 10 -23 J/K

• We are going to explore the average speed of the molecules in an ideal gas
• We want to examine the average effect of an individual molecule, not the aggregate
• Physics looks at the gas laws from the perspective of the work which can be accomplished by changes in gas states
• We also want SI Unit consistency

1.
Gases consist of large numbers of molecules in continuous, random motion
2.
There are no attractive or repulsive forces between gas molecules
3.
Energy is transferred only by collisions
4.
The size of the molecules is negligible
5.
The kinetic energy of the molecules is proportional to the gas temperature

• Gas pressure comes from the transfer of momentum to the walls of the container during collisions (P = F/A)
• This is a three-dimensional problem. Consider a cube of volume V with faces of area A
• On average, half the molecules moving in each direction will be moving toward a face, half will be moving away
• Assumes equal distribution of x, y, and z motion

• The average number of collisions during time t can be expressed as
– the number of molecules within a cube of size
A times |v x
|t (those which will hit the wall)
– times the average molecular density in the space (N/V)
– times ½ (half move toward, half move away)
½ (N/V)(A |v x
|t)

• For a perfectly elastic collision, each molecule will transfer 2m|v x
| momentum
½ (N/V)(A |v x
|t) 2m|v x
|
• The change in momentum will be equal to the impulse (force times time), pressure is equal to force divided by area
P = (N/V) mv x
2

• From the previous slide
P = (N/V) mv x
2
PV = N mv x
2
• Since (v 2 ) ave
= (v x
2 ) ave
+ (v y
2 ) ave
+ (v z
2 ) ave extend the solution to three dimensions
PV = N m/3 (v 2 ) ave
= 2/3 N (½ m (v 2 ) ave
)

• With KE = ½ m(v 2 ) ave we can rewrite
PV = 2/3 KE
• With the ideal gas law PV = Nk
B
T (on a molecular basis)
KE = 3/2 k
B
T

• Which shows that the average kinetic energy per molecule depends only on temperature, not pressure or volume
• If you solve for velocity v rms
= √(v ave
) 2 = √(3 k
B
T/m)
• This is the root-mean-square speed
• Molecules of different mass will have the same KE but different v rms

• The previous analysis assumed a monatomic ideal gas, where the only energy is translational
• The internal energy of a monatomic gas is just the translational energy
U = 3/2 nRT

• Not all the gas molecules will have the same temperature
• The speeds follow the
Maxwell-Boltzmann distribution
• Hotter = faster, but more spread in the speeds
Image from Superborsuk - Wikipedia

• Derivation is beyond our scope f(v) = 4 π(m/2πkT) 3/2 v 2 e -mv2/2kT
• Substituting ε = 1/2mv 2 f(v) = 8 π/m(m/2πkT) 3/2 ε e ε/2kT
• The peak will occur where ε = kT
• Remember: m is the mass of one atom or molecule (kg)

• Most probably speed would be ( ε = kT) v mp
= √(2kT/m)
• Average speed would be v ave
= √(8kT/πm)
• Root-mean-square speed would be v rms
= √(3kT/m)

rms
Gas
H
2
He
H
2
O
Ne
N
2
, CO
NO
O
2
CO
2
O
3 v rms
(m/s at 20 ºC)
1902
1352
637
602
511
494
478
408
390

• In addition to KE, polyatomic gases have vibrational modes and rotational modes
• At the molecular level, these quantities are quantized, yielding predicable energy level transitions
• Radio scientists take advantage of these signatures to detect molecules in space or in our own atmosphere (Ozone)

• A plasma is partially ionized gas, where some of the electrons are free (dissociated) from their parent atoms, which become ions
• Ions always have much more mass than the free electrons, so v e
>> v ions
• Electromagnetic forces do play a role in the behavior of a plasma
• Although charges have been separated, large concentrations of plasma are considered electrically neutral

Image courtesy NASA
Energy

• Much of the upper atmosphere (and most of the universe) is considered a plasma, not a gas
• Electromagnetic radiation (photons) carries energy – collides with molecules
• A steady supply of high-energy photons can break the electron-nucleus bond

• Electrons are “bound” to nuclei
• This is called the electron binding energy
• The structure of the atom determines the bond strength of a particular electron
– The binding energy increases with increasing atomic number from H through Fe, slowly decreasing thereafter

• Hydrogen is the most abundant element in the universe. The binding energy of H is
13.6 eV
• Since E = hf, f = E/h
• 13.6 eV is the energy of a photon with frequency ~ 3.29 x 10 15 Hz
• The wavelength would be ~ 90 nm, or
Extreme UV (EUV) radiation

• The electron volt is the energy it would take to move one electron through a potential of one volt
E = q x V
1 eV = 1.602 x 10 -19 C x 1 V
1 V = 1 J/C
1 eV = 1.602 x 10 -19 J

Name
Ultraviolet A
Near
Ultraviolet B
Middle
Ultraviolet C
Far
Vacuum
Extreme
Abbreviation Wavelength (nm) Energy (eV)
UVA 400 - 320 3.10 - 3.94
NUV 400 - 300 3.10 - 4.13
UVB
MUV
UVC
FUV
VUV
EUV
320 - 280
300 - 200
280 - 100
200 - 122
200 - 10
121 - 10
3.94 - 4.43
4.13 - 6.20
4.43 - 12.4
6.20 - 10.2
6.20 - 124
10.2 - 124

• Photons with energies above 13.6 eV have the potential to “knock off” an electron from an atom or molecule
• This is considered ionizing radiation
Image courtesy J. Carlton Gallawa

• Scientists like to take common words and use them in very specific ways
• The term radiation has taken on two distinct meanings
– Electromagnetic radiation
– Particles released through radioactive decay

• Electromagnetic waves (photons) cover a spectrum from Radio to Gamma-rays
– Mostly harmless at low energies
– Above ~ 13.6 eV, photons can ionize matter
• This can cause biological damage, depending on the time and amount of exposure
• UV, X-rays, and Gamma-rays

• EM radiation has velocity, wavelength, and frequency, therefore they are waves
• EM radiation are also discrete packets of energy called photons (E = h ·f)
• At lower energies (Radio, Visible), the wave properties tend to dominate
• At higher energies (UV, X-ray, Gamma), the particle properties are more obvious

• A gas with as little as 1% ionization can behave as a plasma
• Constituents are electrons, ions, and neutral atoms (neutrals)
• Remember that the electrons are much smaller than the ions and neutrals
– Mass of one proton ~ 1836 times the mass of one electron

• You can categorize plasma as either
– Thermal plasma: electrons and other constituents in thermal equilibrium
– Non-thermal plasma: electrons are at much higher temperature than ions and neutrals
• Preconception: plasmas are very high temperature phenomenon. Not true!

th

• The Thermosphere is sparsely populated
(but still a measurable atmosphere)
• The gases in the Thermosphere will readily absorb ultraviolet and X-rays, increasing their speeds, making the temperature climb to 500 – 1500 ºC
• Since there are so few molecules, if you were to be exposed to the Thermosphere, the energy transfer would be minimal

• The number of molecules per volume in the
Thermosphere is about one billionth of the number of molecules near the Earth’s surface
• The probability that the molecules will collide, transfer their energy and cause heating is extremely low (large mean free path )
• Therefore, the temperatures recorded in the thermosphere are good measures of molecular energy but not comparable to the ability of the atmosphere to transfer heat (energy)