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Gases and Heat

Gases and Heat. Chapter 18. Boltzmann’s Version of pV=nRT. pV = Nk B T N = Number of molecules k B = Boltzmann’s Constant (1.38 X 10 -23 J/K). Mean Free Path. Average distance between collisions Also used to describe electrons moving through wires Light passing through glass, water.

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Gases and Heat

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  1. Gases and Heat Chapter 18

  2. Boltzmann’s Version of pV=nRT pV = NkBT N = Number of molecules kB = Boltzmann’s Constant (1.38 X 10-23 J/K)

  3. Mean Free Path • Average distance between collisions • Also used to describe electrons moving through wires • Light passing through glass, water

  4. l = 1 4\/2 p (N/V)r2 l = mean free path r = 0.5 X 10-10 m (monoatomic gases) 1.0 X 10-10 m (diatomic gases)

  5. Example A nitrogen molecule (N2, diatomic) is at 1.0 atm of pressure and 20oC • Convert the temperature and pressure to the proper units • Calculate the value N/V using Boltzmann’s Equation • Calculate the mean free path of the molecule.

  6. Root-Mean Square Speed • Velocity has a direction • Overall, in a container of gases, the velocity is zero • Average speed is not zero vrms = \/(v2)avg vrms = 3kBT m m is the mass of one molecule (kg)

  7. Example 1 Nitrogen molecules (N2) are at room temperature, 20oC. • Calculate the mass of one molecule (kg) • Calculate the rms speed

  8. Example 2 Cesium atoms can be cooled to 1.0 mK (m is 10-6) • Calculate the mass of 1 cesium atom • Calcuate the rms speed

  9. Translational Energy Eavg = 3/2 kBT (for one molecule) Eavg = 3/2NkBT = 3/2 nRT (for all molecules) N = number of molecules n = number of moles

  10. Example A balloon contains 2.00 grams of Helium at 25.0oC • Calculate the average energy of one atom of Helium. • Calculate the average energy of the sample.

  11. Second Law of Thermodynamics 2nd Law • Natural processes tend to move toward a state of greater disorder • Heat goes hot to cold (Clausius) • No device converts all heat to work (Kelvin-Planck) DS >0

  12. Calculating Entropy DS = Q T • Reversible process • Constant Temperature • T in Kelvin

  13. Calculating Entropy: Example 1 How much entropy is produced when 30 grams of ice melts at 0oC? Q = mLfusion Q = (0.030 kg)(3.33 X 105 J/kg) Q = 9,990 J DS = 9,990 J = 36.6 J/K 273 K

  14. Calculating Entropy: Example 2 How much entropy is produced when 500 g of water boils and vaporizes at 100oC? Q = mLvaporization Q = (0.500 kg)(22.6 X 105 J/kg) Q = 11.3 X 106 J DS = 11.3 X 106 J = 3030 J/K 373 K

  15. Calculating Entropy: Example 3 How much entropy is produced when 300 g of lead melts at 327 oC? The latent heat of fusion of lead is 2.45 X 104 J/kg Q = mLvaporization Q = (0.300 kg)(2.45 X 104 J/kg) Q = 7.35 X 103 J DS = 7.35 X 103 J = 12.3 J/K 600 K

  16. Entropy and the Universe • Natural processes tend to move towards a state of greater disorder • DSuniverse > 0 • Only local order can be produced • Cleaning your room example • Eventually the entire universe will be the same temperature (no heat engines possible). Heat death.

  17. Thermal Pollution • Thermally polluting power plants • Coal plants • Oil plants • Nuclear plants • Non-thermally polluting power plants • Hydroelectric • Tidal energy • Wind • Solar

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