![The Ideal Gas Law P V = N k B T P = pressure in N/m 2 (or Pascals ) V = volume in m 3 N = number of molecules T = absolute temperature in K k B = Boltzmann’s constant = 1.38 x 10 -23 J/K Note: P V has units of N-m or J (energy!) P V = n R T n = number of moles R = ideal gas constant = N A k B = 8.31 J/mol/K I don't understand why we have the ideal gas law when basically no gases are ideal. It confuses me [old comment].](https://image.slidesharecdn.com/lecture24-111222210229-phpapp02/85/Lecture24-9-320.jpg)
Lecture24
- 1. Physics 101: Lecture 24 Ideal Gas Law and Kinetic Theory Today’s lecture will cover Textbook Chapter 13.5-13.7 EXAM III
- 2. Aside: The Periodic Table
- 3. The Periodic Table Explained ? proton neutron electron Look carefully
- 4. Energy vs Mass He (m=4.0026 u) O (M=15.9995 u) So energy is the same as mass somehow ?? 4 x He = 16.01 u Mass difference = 0.01 u = binding energy E = mc 2 (phys 102)
- 5. Molecular Picture of Gas Gas is made up of many individual molecules Number density is number of molecules/volume: N/V = /m is the mass density m is the mass for one molecule Number of moles : n = N / N A N A = Avogadro’s Number = 6.022x10 23 mole -1 Mass of 1 mole of “stuff” in grams = molecular mass in e.g., 1 mole of N 2 has mass of 2x14=28 grams moles! I hate moles!
- 6. Atomic Act I Which contains the most molecules ? 1. A mole of water (H 2 O) 2. A mole of oxygen gas (O 2 ) 3. Same H 2 O O 2 correct
- 7. Atomic Act II Which contains the most atoms ? 1. A mole of water (H 2 O) 2. A mole of oxygen gas (O 2 ) 3. Same H 2 O (3 atoms) O 2 (2 atoms) correct
- 8. Atomic Act III Which weighs the most ? 1. A mole of water (H 2 O) 2. A mole of oxygen gas (O 2 ) 3. Same H 2 O (M = 16 + 1 + 1) O 2 (M = 16 + 16) correct
- 9. The Ideal Gas Law P V = N k B T P = pressure in N/m 2 (or Pascals ) V = volume in m 3 N = number of molecules T = absolute temperature in K k B = Boltzmann’s constant = 1.38 x 10 -23 J/K Note: P V has units of N-m or J (energy!) P V = n R T n = number of moles R = ideal gas constant = N A k B = 8.31 J/mol/K I don't understand why we have the ideal gas law when basically no gases are ideal. It confuses me [old comment].
- 10. Ideal Gas Law ACT I PV = nRT You inflate the tires of your car so the pressure is 30 psi, when the air inside the tires is at 20 degrees C. After driving on the highway for a while, the air inside the tires heats up to 38 C. Which number is closest to the new air pressure? 1) 16 psi 2) 32 psi 3) 57 psi Careful, you need to use the temperature in K P = P 0 (38+273)/(20+273)
- 11. Ideal Gas Law: ACT II pV = nRT A piston has volume 20 ml, and pressure of 30 psi. If the volume is decreased to 10 ml, what is the new pressure? (Assume T is constant.) 1) 60 2) 30 3) 15 V=20 P=30 V=10 P=?? When n and T are constant, pV is constant (Boyle’s Law)
- 12. Balloon ACT 1 What happens to the pressure of the air inside a hot-air balloon when the air is heated? (Assume V is constant) 1) Increases 2) Same 3) Decreases Balloon is still open to atmospheric pressure, so it stays at 1 atm
- 13. Balloon ACT 2 What happens to the buoyant force on the balloon when the air is heated? (Assume V remains constant) 1) Increases 2) Same 3) Decreases F B = V g is density of outside air!
- 14. Balloon ACT 3 What happens to the number of air molecules inside the balloon when the air is heated? (Assume V remains constant) 1) Increases 2) Same 3) Decreases PV = NkT P and V are constant. If T increases N decreases.
- 15. Lecture 24, Preflight 2 In terms of the ideal gas law, explain briefly how a hot air balloon works. The flame lifts the balloon because it gets rid of the air inside, making it lighter inside. Dumbledore has cast levitation charms (which is pronounced leviosá not leviosa) on every hot air balloon. hot air rises. The fire heats up the air inside the balloon. The air rises and pushes on the inside of the balloon which makes the pressure higher on the inside than the outside. Since there is more pressure pushing up than pushing down, the balloon rises. Note! this is not a pressure effect, it is a density effect. As T increases, the density decreases the balloon then floats due to Archimedes principle. The pressure remains constant!
- 16. Ideal Gas Law: Demos pV = nRT When T is constant, pV is constant (Boyle’s Law) Boyle’s law demo When p is constant, V is proportional to T Hot air balloon, helium and oxygen in LN 2 When V is constant, p is proportional to T Explosion!
- 17. Kinetic Theory: The relationship between energy and temperature (for monatomic ideal gas) L For N molecules, multiply by N Note KE = ½ m v 2 = 3/2 m v x 2 Using PV = NkT 〈〉 means average . kT/2 energy per degree of freedom = equipartition theorem
- 18. Preflight 1 Suppose you want the rms ( root-mean-square ) speed of molecules in a sample of gas to double. By what factor should you increase the temperature of the gas? 1. 2 2. 3. 4 If v doubles, v 2 quadruples Therefore, T quadruples root-mean-square? correct
- 19. Example What is the rms speed of a nitrogen (N 2 ) molecule in this classroom? v = 510 m/s = 1150 mph!
- 20. Summary Ideal Gas Law PV = n R T P = pressure in N/m 2 (or Pascals) V = volume in m 3 n = # moles R = 8.31 J/ (K mole) T = Temperature (K) Kinetic Theory of Monatomic Ideal Gas <K tr > = 3/2 k B T