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