Heat vs Temperature

1. Heat vs Temperature Why do we think space is so cold?

2. 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

3. 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

4. 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!

5. 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

6. 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

7. 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 1.4 Calibration of Thermometers

8. 1.5 Temperature Scales • Fahrenheit and Celsius scales were originally based on the freezing and boiling points of water

9. 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

10. 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

11. 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

12. 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!

13. 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

14. 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

15. 1.6.1 Some examples

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 2.4 Kinetic Theory of Gases • Gases consist of large numbers of molecules in continuous, random motion • There are no attractive or repulsive forces between gas molecules • Energy is transferred only by collisions • The size of the molecules is negligible • The kinetic energy of the molecules is proportional to the gas temperature

25. 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

26. 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)

27. 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

28. 2.5.3 Looking at all dimensions • From the previous slide P = (N/V) mvx2 PV = Nmvx2 • Since (v2)ave = (vx2)ave +(vy2)ave +(vz2)ave extend the solution to three dimensions PV = Nm/3 (v2)ave = 2/3 N (½ m (v2)ave)

29. 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

30. 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

31. 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

32. 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

33. 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 εe-ε/2kT • The peak will occur where ε = kT • Remember: m is the mass of one atom or molecule (kg)

34. 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)

35. Vrms of atmospheric gases

36. 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)

37. 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

38. The Four States of Matter Energy Image courtesy NASA

39. 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

40. 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

41. 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

42. 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 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

43. 3.1.2.2 The UV Spectrum

44. 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

45. 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

46. 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

47. 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

48. 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

49. 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!

50. Plasma – The 4th State of Matter