1. AP Physics Mr. Jean November 22 nd, 2011

2. The plan: Ideal Gas law questions Quantum States of matter Expand Ideal Gas ideas Application to KE equations

3. Question: A spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and having a volume of 125cm 3 is at 22 o C. It is tossed into an open fire. When the temperature reaches 195 o C what is the pressure in the can? Assume NO volume change. Assume Ideal Gas.

4. Solution: Ideal Gas Law PV = nRT No air escapes during the compression, so that ‘nR’ remain constant. Thus we can eliminate them from both sides of the equation. P i V i = P f V f T i T f

5. Solution: P f = (T f / T i ) P i P f = 320 kPa

6. Question to consider at Home: In air, the molecular mass of oxygen molecules is 32 g/mol; the molecular mass of nitrogen molecules is 28 g/mol. Which molecules are traveling faster on average? a. a.Oxygen b. b.Nitrogen c. c.Same speed

7. Equipartition Theorem “The total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium.” a. a.Treat these as “independent”: – – x & y axis (for translational KE). b. b.“parts” means the: – – translational, rotational, vibrational characteristics of atoms and molecules.

8. Thermal energy must be comparable to the different (quantum) energy levels From section 21.4: diatomic hydrogen Y-axis: heat added, divided by temperature change (per mole) Units: J/mol  K

9. Translational KE: Calculate the average kinetic energy of one nitrogen molecule at 300K? Helpful Formula: E k = B/A (RT) B/A = proper quantum level ratio R = Ideal gas law constant T = Temperature in Kelvin

10. Translational KE: Calculate the average kinetic energy of one nitrogen molecule at 300K? Start by considering the quantum state of the matter. This is normally done by using a table or a graph. (Either 3/2, 5/2 or 7/2) Second use the proper ratio to calculate the total energy.

11. Solution Assume nitrogen behave as an ideal gas, then Ek = 3/2 R T = (3/2) 8.3145 J/(mol K) * 300 K = 3742 J / mol (or 3.74 kJ/mol)

12. Questions to Consider: Consider the ideal gas laws. How do pressure and volume questions relate? a. a.What relationship should they have? b. b.What type of reaction would you expect if pressure increases while volume decreases with particles being lost? What is a PV diagram?

13. Pressure & Volume: Check out this a. a.Demonstration 5.1 b. b.Demonstration 5.2