1. Gas Laws and Thermal properties of matter
PV=nRT

2. Equations of State
State Variables – Variables that describe the condition or state a material is in (macroscopic)
Ex. Volume, Pressure, Temperature
Equations of State – shows the relationship of different state variables
Can get complicated but made simpler through approximations
Ex. Equations of state for a solid

3. Ideal Gas
An ideal gas is composed of randomly moving, non- interacting point particles.
Difficult to describe gas in terms of mass
Easier to use
Where n is the number of moles and
M is the molar mass (mass per mole of gas)
For those who’ve forgotten one mole is NA=6.022x1023 atoms of 1 element

5. Ideal Gas
Volume is proportional to the number of moles of the gas (keeping Pressure and temperature the same)
Volume is inversely proportional to pressure (keeping number of moles and temperature the same)
Pressure is proportional to the absolute temperature (keeping volume and number of moles the same)

6. Ideal Gas Equation Where R is the gas constant R=8.314J/molK
This equation will work for an ideal gas for all pressures and temperatures
For real world gasses this still holds for low pressures and temperatures
Its off by a few percent at higher P
Note how PV = energy

7. Example- Mass of air in a Scuba Tank
A scuba tank usually has a volume of 11.0L a gauge pressure of 2.10x107 Pa when full. The “empty” tank contains 11.0L of air at 21.0oC at 1 atm. A compressor pumped air into the tank, increasing its temperature to 42.0oC and the pressure to 2.11x107Pa. What mass of air was added? (air is 78% N, 21% O, 1% misc. Average molar mass is 28.8g/mol)

8. Example

9. Example – Young and Freedman 18.3
A cylindrical tank has a tight fitting piston that allows its volume to change. The tank originally contains 0.110m3 of air at a pressure of 3.40atm.
The piston is slowly pulled out until the tank has a volume of 0.390m3. If temperature remains constant what is the final value of the pressure?

10. PV=nRT=constant

11. Boltzmann’s Constant When dealing with macroscopic variables
Sometimes instead of n, number of moles, you have N, number of molecules
Where kB is boltzmann’s constant
Look at my magnificent beard

12. Van der Waals Equation Corrects some omissions in ideal gas equation
Where b is the volume of 1 mole of gas and a is the attractive forces between the molecules
If n/V is small, the gas is dilute and it reduces to the ideal gas equation

13. Kinetic Energy of a gas Gas molecules are always in motion
Kinetic energy of molecules proportional to its temperature
That means gas in a container also has energy
Assumptions
Volume V has large number N of identical molecules
Molecules are point particles
Molecules are in constant motion and collide elastically
Container walls are rigid and do not move

14. Kinetic Energy of Gas
Collision of molecules with container is what causes pressure.
CHEAT: instead of using time the molecule is in contact with the wall, we can use the time it takes for the molecule to impact the wall again
Molecule needs to travel 2d where d is the side of the container

15. Kinetic Energy of Gas That is the force of 1 molecule
Total force is will be
Where N is the number of molecules

16. Kinetic Energy of Gas Average velocity squared is Total force is
We can generalize this for velocity in all directions

17. Kinetic Energy of Gas
Average velocity squared will equal (Pythagorean for 3d)
Somewhat cheat: because gas molecules move randomly, the probability of moving in any direction is the same. Average velocity in one direction will equal average velocity in all directions

18. Kinetic Energy of Gas
Rearrange terms
Divide by Area

19. Rearrange Terms
Holds to some extent for liquids and even solids

20. Root Mean Squared Speed
Average of velocities squared (not the square of the average velocities)

21. Example – Young and Freedman 18.36
Martian Climate- Atmosphere of Mars is mostly CO2 (M=44.0g/mol) under a pressure of 650 Pa, which we shall assume remains constant. The temperature varies from 0.0oC to -100oC througout the year. Over the course of a year, what are the ranges of (a) the rms speeds of the CO2 molecules (b) the density in mol/m3 of the atmosphere?

22. Example
0oC
-100oC

23. Example
Density in mol/m3
0oC
100oC

24. Phase Changes of Matter
We now relate phase changes with pressure as well
A change in phase will occur when the system is in phase equilibrium
one is to one relationship between pressure and temperature
We can plot PvsT on a graph to create a phase diagram

25. Phase Diagram of Water

26. Phase Diagram of CO2

27. Phase Diagram
Triple Point- the only Pressure and Temperature where all three phases can exist
Critical Point – Differences in solid and liquid phase disappear

28. PVT Surfaces

29. Example – Young and Freedman 18.50
Puffy Cumulous clouds which are made of water droplets, occur at lower altitudes of the atmosphere. Wispy Cirrus clouds, made of ice droplets, only occur at higher altitudes. Find the Altitude y above which only cirrus clouds can occur. On a typical day and an altitude less than 11 km, the temperature at any given altitude is T=T0-αy where T0=15oC and α=6.0oC/1000m

30. Giancoli 13-40
A helium filled balloon is escapes a child's hand at sea level and 20.0oC. When it reaches an altitude of 3000m where the temperature is 5.00oC and the pressure is only atm, how will its volume compare to that at sea level?

31. Young and Freedman 18.20
With the assumption that the air temperature is a uniform 0.0oC, what is the density of the air at an altitude of 1.00km as a percentage of the density at the surface?

32. Giancoli 13-60
Two isotopes for uranium are 235U and 238U. They can be separated by gas diffusion by combining them with fluorine to form UF6. Calculate the ratio of the RMS speeds of these molecules for the two isotopes at constant T.