Heat vs Temperature
Why do we think space is so cold?
Dispelling the myths
• 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
1.0 Heat
• 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
1.1 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!
1.2 Thermometers
• 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
1.3 Construction of Thermometers
• 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
1.4 Calibration of Thermometers
• 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
1.5 Temperature Scales
• Fahrenheit and Celsius scales were originally
based on the freezing and boiling points of water
Scale
Freezing Point
Boiling Point
Fahrenheit
32 ºF
212 ºF
Celsius
0 ºC
100 ºC
Kelvin
273.15 K
373.15 K
1.5.1 Definition of Kelvin Scale
• 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 H20 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
1.5.2 Why kelvins?
• 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
1.5.2.1 Kelvin trivia
• 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
1.5.2.2 More Kelvin trivia
• 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!
1.5.3 Temperature Conversion
• Converting between the different scales is
a simple algebra problem
TK = TC + 273.15
ΔTC = ΔTK
TF = 9/5 TC + 32
TC = 5/9 (TF – 32)
ΔTC = 5/9 ΔTF
1.6 Color Temperature
• 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
1.6.1 Some examples
Temperature
Source
1700 K
Match flame
1850 K
Candle flame
2700 - 3300 K
Incandescent light bulb
4100 K
Moonlight
5000 K
Horizon daylight
5500 - 6000 K
Typical daylight
6500 K
Overcast daylight
1.6.1.1 CFL choices
• 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
1.6.2 Photography and Color Temp
• 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
1.6.3 Implications of Mismatch
• 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
2.0 Temperature of a Gas
• For gases, temperature is proportional to
the kinetic energy of the molecules
• Since KE = ½ mv2, the faster the
molecules move, the higher the
temperature
• Twice the KE yields twice the temperature
2.1 What is an Ideal Gas?
•
•
•
•
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
2.2 Ideal Gas Law (Chemistry)
• 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
2.3 Ideal Gas Law (Physics)
• In Physics, PV = NkBT
– P is pressure (in pascals)
– V is volume (in meters-cubed)
– N is the number of molecules
• (N = n·NA, where NA is Avogadro’s Number)
– T is the temperature (kelvins)
– kB is Boltzmann’s constant
• 1.38 x 10-23 J/K
2.3.1 Why change notation?
• 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
2.4 Kinetic Theory of Gases
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
2.5 Assumptions
• 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
2.5.1 Collisions with the wall
• The average number of collisions during
time t can be expressed as
– the number of molecules within a cube of size
A times |vx|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 |vx|t)
2.5.2 Momentum transfer
• For a perfectly elastic collision, each
molecule will transfer 2m|vx| momentum
½ (N/V)(A |vx|t) 2m|vx|
• The change in momentum will be equal to
the impulse (force times time), pressure is
equal to force divided by area
P = (N/V) mvx2
2.5.3 Looking at all dimensions
• From the previous slide
P = (N/V) mvx2
PV = N mvx2
• Since (v2)ave = (vx2)ave + (vy2)ave + (vz2)ave
extend the solution to three dimensions
PV = N m/3 (v2)ave = 2/3 N (½ m (v2)ave)
2.5.4 Introduce Kinetic Energy
• With KE = ½ m(v2)ave we can rewrite
PV = 2/3 KE
• With the ideal gas law PV = NkBT (on a
molecular basis)
KE = 3/2 kBT
2.5.5 Average velocity
• Which shows that the average kinetic
energy per molecule depends only on
temperature, not pressure or volume
• If you solve for velocity
vrms = √(vave)2 = √(3 kBT/m)
• This is the root-mean-square speed
• Molecules of different mass will have the
same KE but different vrms
2.5.6 Monatomic gas
• 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
2.5.7 Maxwell-Boltzmann
Distribution
• 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
2.5.8 The equation
• Derivation is beyond our scope
2/2kT
3/2
2
-mv
f(v) = 4π(m/2πkT) v e
• Substituting ε = 1/2mv2
f(v) = 8π/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)
2.5.9 Different speeds
• Most probably speed would be (ε = kT)
vmp = √(2kT/m)
• Average speed would be
vave = √(8kT/πm)
• Root-mean-square speed would be
vrms = √(3kT/m)
Vrms of atmospheric gases
Gas
H2
He
H2O
Ne
N2, CO
NO
O2
CO2
O3
vrms (m/s at 20 ºC)
1902
1352
637
602
511
494
478
408
390
2.6 Spectral lines
• 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)
3.0 Plasma ≠ Gas
• 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 ve >> vions
• 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
The Four States of Matter
Energy
Image courtesy NASA
3.1 How does a plasma form?
• 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
3.1.1 Why does plasma form?
• 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
3.1.2 Binding Energy
• 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 1015 Hz
• The wavelength would be ~ 90 nm, or
Extreme UV (EUV) radiation
3.1.2.1 The Electron Volt
• The electron volt is the energy it would
take to move one electron through a
potential of one volt
E=qxV
1 eV = 1.602 x 10-19 C x 1 V
1 V = 1 J/C
1 eV = 1.602 x 10-19 J
3.1.2.2 The UV Spectrum
Name
Abbreviation
Wavelength (nm)
Energy (eV)
Ultraviolet A
UVA
400 - 320
3.10 - 3.94
Near
NUV
400 - 300
3.10 - 4.13
Ultraviolet B
UVB
320 - 280
3.94 - 4.43
Middle
MUV
300 - 200
4.13 - 6.20
Ultraviolet C
UVC
280 - 100
4.43 - 12.4
Far
FUV
200 - 122
6.20 - 10.2
Vacuum
VUV
200 - 10
6.20 - 124
Extreme
EUV
121 - 10
10.2 - 124
3.1.3 Ionizing Energy
• 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
3.1.4 Radiation
• 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
3.1.4.1 EM Radiation
• 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
3.1.4.1.1 Wave-Particle Duality
• 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
3.2 Characteristic of a plasma
• 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
3.3 Plasma Temperature
• 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!
Plasma – The 4th State of Matter
4.0 So, Why is Space Hot?
• 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
4.1 All about heat vs temp
• 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)