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 PointFahrenheit 32 ºF 212 ºFCelsius 0 ºC 100 ºCKelvin 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 problemTK = TC + 273.15

ΔTC = ΔTK

TF = 9/5 TC + 32TC = 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 examplesTemperature 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 Gases1. Gases consist of large numbers of

molecules in continuous, random motion2. There are no attractive or repulsive

forces between gas molecules 3. Energy is transferred only by collisions4. The size of the molecules is negligible5. 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| momentum½ (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 slideP = (N/V) mvx

2

PV = N mvx2

• Since (v2)ave = (vx2)ave + (vy

2)ave + (vz2)ave

extend the solution to three dimensionsPV = 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 velocityvrms = √(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

f(v) = 4π(m/2πkT)3/2v2e-mv2/2kT

• 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 bevave = √(8kT/πm)

• Root-mean-square speed would bevrms = √(3kT/m)

Vrms of atmospheric gasesGas vrms (m/s at 20 ºC)H2 1902He 1352

H2O 637Ne 602

N2, CO 511NO 494O2 478

CO2 408O3 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

Image courtesy NASA

Energy

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 = q x V1 eV = 1.602 x 10-19 C x 1 V1 V = 1 J/C1 eV = 1.602 x 10-19 J

3.1.2.2 The UV SpectrumName 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)