17-1 Ideal Gases. Gases are the easiest state of matter to describe - All ideal gases exhibit similar behavior.

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1 17-1 Ideal Gases Gases are the easiest state of matter to describe - All ideal gases exhibit similar behavior. An ideal gas is one that is thin enough, that the interactions between molecules can be ignored. 3

2 17-1 Ideal Gases If volume of an ideal gas is held constant, we find that the pressure increases with temperature: 4

3 17-1 Ideal Gases If volume and temperature are kept constant, but more gas is added (such as in inflating a tire or basketball), the pressure will increase: 5

4 17-1 Ideal Gases Finally, if the temperature is constant and the volume decreases, the pressure increases: 6

5 17-1 Ideal Gases Combining all three observations, we get where k is called the Boltzmann constant: Rearranging: 7

6 17-1 Ideal Gases Experimentally, the number of entities (atoms or molecules) in a mole is given by Avogadro s number: Therefore, n moles of gas will contain molecules: 8

7 17-1 Ideal Gases Avogadro s number and the Boltzmann constant can be combined to form the universal gas constant and an alternative equation of state: 9

8 17-2 Kinetic Theory Kinetic theory relates microscopic quantities (position, velocity) to macroscopic ones (pressure, temperature). Assumptions: 1.N identical molecules of mass m are inside a container of volume V; each acts as a point particle. 2. Molecules move randomly and always obey Newton s laws. 3. Collisions with other molecules and with the walls are elastic. 10

9 17-2 Kinetic Theory Pressure is the result of collisions between the gas molecules and the walls of the container. Depends on the mass and speed of the molecules, and on the container size: 11

10 17-2 Kinetic Theory Not all molecules in a gas will have the same speed; their speeds are represented by the Maxwell distribution, and depend on the temperature and mass of the molecules. 12

11 17-2 Kinetic Theory Replace the speed in the previous expression for pressure with average speed: Considering the other two directions, Pressure in gas is proportional to the average kinetic energy of its molecules 13

12 17-2 Kinetic Theory Comparing this expression with the ideal gas law allows us to relate average kinetic energy and temperature: The square root of (rms) speed is called the root mean square 14

13 17-2 Kinetic Theory Solving for the rms speed gives: 15

14 17-2 Kinetic Theory Rms speed is slightly greater than the most probable speed and the average speed. 16

15 17-2 Kinetic Theory Internal energy of ideal gas is sum of the kinetic energies of all its molecules. In the case where each molecule consists of a single atom, this is: 17

16 17-5 Latent Heats When two phases coexist, the temperature remains the same even if a small amount of heat is added. Instead of raising the temperature, the heat goes into changing the phase of the material melting ice, for example. 18

17 17-5 Latent Heats Heat required to convert from one phase to another is called the latent heat. Latent heat, L, is the heat that must be added/removed to one kilogram of a substance to change its phase During the conversion process, the temperature of the system remains constant. 19

18 17-5 Latent Heats Latent heat of fusion: heat needed to go from solid to liquid Latent heat of vaporization: heat needed for liquid to gas. 20

19 43 Answer: 316 K

20 44 Answer: 19.8 K

21 45 Answer: 362 kj

22 46 Answer: 5.9 kj