1. PHY1039 Properties of Matter van der Waals Gas 16 February, 2012 Lecture 4

2. Boltzmann Distribution of Molecular Speeds in a Gas Figure from “Understanding Properties of Matter” by M. de Podesta

3. Boltzmann Distribution of Speeds in a Gas Figure from “Understanding Properties of Matter” by M. de Podesta Average speed increases as a function of T 1/2 At a given T, lighter molecules have a higher average speed.

4. Types of Thermodynamic Wall P 1 V 1 T 1 P 2 V 2 T 2 P 1 V 1 T 1 Time P 2 V 2 T 2 No change in the state variables. P 1 V 1 T 1 P 2 V 2 T 2 P 1 eq V 1 T eq Time P 2 eq V 2 T eq State variables change over time. The temperature on either side of the wall is at an equilibrium value, T eq. System 1 System 2

5. No Gas Is Ideal ! Constant P Constant TConstant V V P P V TT V T High P Low P P Low V High V

6. Potential Energy for Non-Charged Atoms/Molecules r  r  Potential Energy There is also kinetic energy, which is the energy of motion. Figure from “Understanding Properties of Matter” by M. de Podesta ~ r -6 Relevant to gases, liquids and solids (e.g. Ar, Xe, CO 2 ) Potential energy: Force between molecules:

7. van der Waals Parameters of Selected Gases Gas a (L 2 atm. mol -2 ) b (L mol -1 ) Air1.40.039 Ammonia4.170.037 Argon1.350.032 Carbon Dioxide3.590.043 Ethane5.490.064 Helium0.0340.024 Hydrogen0.2440.027 Nitrogen1.390.039 Oxygen1.360.032 Xenon4.190.051

8. it.wikipedia.org/wiki/Legge_di_Van_der_Waals PV diagram for CO 2 n = 1 V (dm 3 ) P (kPa) 1 atm.  101 kPa

9. Phase Diagram of CO 2 Gas condenses when attractive intermolecular bond energies are comparable to or greater than thermal (i.e. kinetic) energy, 3/2 kT. Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html