Kinetic Theory of Gases: Microscopic Behavior Influencing Macroscopic Variables

1. Written Quiz 1:On your OWN piece of paper, define the following: • Atom • Molecule • Macroscopic • Microscopic • Readings for the next topics (books are on reserve at the Library): • Review molecule definition of matter (Giancoli, “Physics 6th ed.” Page 353, 367-68 ) • Differentiate particle properties as intensive of extensive (Addison and Wesley, “Thermodynamics, Kinetic Theory, and Statistical Thermodynamics” Page 3) • State the 3 phases of matter solid, liquid, and gas (Giancoli, “Physics 6th ed.” Page 255)

2. Kinetic Theory of Gases • Kinetic theory uses math to determine the affects of gas on macroscopic variables such as pressure, temperature and volume based on atom behavior at the microscopic level. • Kinetic theory is a sub topic of statistical mechanics developed by Robert Boyle, Daniel Bernoulli, James Joule, A. Kronig, Rudolph Clausis and Clerk Maxwell – to name a few. • Kinetic theory is needed because the quantity and behavior of microscopic particles is too chaotic to model without taking advantage of statistical mechanics

3. Brownian motion • Random motion of pollen seen by microscope in water, suggests that matter is made up of atoms that are always moving (Video link) • Einstein actually just brought the theory back to life • Perrin used Brownian motion to deduce a quantity for Avogadro's number (N0 = 6 x 1023 particles per mole), linked Brownian motion to kinetic theory and VRMS (root-mean-square) predicted by Einstein

4. Ideal gases • Macroscopic (or thermodynamic) definition of an ideal gas • Boyle’s Law at a constant mass and temperature • Charles Law at a constant mass and pressure • Thus, when mass is constant • Adding • R is the universal gas constant 8.314 joule/mole K • n is the number of moles or moles per gram or moles per m³ • Results in (Equation of State) • Units

5. Ideal gas assumptions at microscopic level • A gas consist of particles called molecules • The molecules are in random motion and obey Newton’s laws of motion • The total number of molecules is large • The volume of the molecules is negligibly small fraction of the volume occupied by the gas • No appreciable forces act on the molecules except during a collision • Collisions are elastic and are of negligible duration

6. Pressure of an Ideal gas • Board Derivation

7. Summary today’s topics in Kinetic Theory • Brownian motion (experimental evidence that atoms exist – pollen in water ) • Ideal gas law(combination of Bolye’s and Charles law – Pv=nRT ) • Ideal gas assumptions (6 of them - works well for low P and T for most gases)

8. Group Problems • What is R and n?Also, what are some units of R and n? • A cylinder contains 100 liters of an ideal gas at 20 °C and a pressure of 200,000 Pascals. A piston lowers the cylinder decreasing the volume to 80 liters and raising the temperature to 25 °C. What is the final pressure? • Show how boyle’s law (pV = constant) and Charles law (V/T = constant) can be combined to yield pV/T = constant • The average velocity of the molecules in a gas must be zero if the gas as a whole and the container are not in translational motion. Explain how it can be that the average speed is not zero?

9. Presentations • Group 1 • Group 2 • Group 3 • Group 4

10. Assignment Solutions • What is R and n and what are their units? • Ris the universal gas constant • R = 8.314 (J/mol-K) • R = 0.0821 (L-atm/mol-K) • R =1.99 (calories/mol-K) • n is the a number of (moles) of a substance that has 6 x 1023molecules of a gas • 2. Ideal Gas Law PV=nRT Ideal Gas Law For System 1 → 2 Relationship must use absolute temperatures (convert to K) P2 = ??? pa P1 = 200,000 pa V2 = 80 L V1 = 100 L T2 = 25 °C T1 = 20 °C

11. Assignment Solutions Continued • Derive PV/T = Constant from Boyle’s and Charles Law • Boyle’s Law at a constant mass and temperature • Charles Law at a constant mass and pressure Solve both relationships for V Graph V V Equation of Line V T