Chapter 12 Temperture, Kinetic Theory, and the Gas Law

1. Chapter 12Temperture, Kinetic Theory, and the Gas Law

2. 12.1 Temperature Operational - measured by thermometer, using physical properties of materials, such as volume change, resistance change and color change

3. Relation among Fahrenheit, Celsius, and Kelvin temperture scales.

4. Logarithmic scale of tremendous range of tempertures in nature.

5. 12.2 Thermal expansion of solids and liquids • p.299 Table 12.1, coefficient of linear and volume(~3*linear) • expansion • Objects expand in all directions as temperature incresass. • Area increases • Size of the hole increases • Volume increase

6. This crack in a concrete sidewalk was created by thermal stress, an indication of how great such stress can be.

7. 12.3 The Ideal Gas Law Ideal gas  no attraction among gas molecules PV = NkT P = pressure of gas , V = volume of gas T =temperature (K) N= number of atoms or molecules in the gas k = 1.38*10-23 J/K P ↑ as T ↑ V ↓ as P ↑ - indepdent of the type of gas Gas – atoms or molecules are widely separate

8. When air is pumped into a deflated tire, its volume increased without pressure change To a certain point, the tire wall resist further expansion and P ↑ with more air. Once the tire is inflated, P ↑ as T ↑

9. Moles and Avogardro’s Number, NA A mole = amount of a substance that contains as many atoms or molecules as there are atoms in exactly 0.012kg of carbon-12. NA = 6.02*1023 /mol A more precise value wait until Einstein’s theory used to determine the size and masses of atoms Example 12.5 How many atoms and molecules are there in a volume of gas at STP? Solutions Given STP  P=1 atm, V=1 m3, T=00C, N = ? N=PV/kT = 1.01*105*1/(1.38*10-23*273) = 2.68*1025

10. NA = 6.02*1023 /mol Macroscopic  like this mole of table tennis balls covering the Earth to a depth of about 35 km !

11. The Ideal Gas Law Restated using Mole R = Universal gas constant = 6.02*1023 *1.38*10-23 = 8.31 J/(mol K) = 1.99 cal/(mol K) = 0.0821 L atm/(mol K) n = number of moles

12. 12.4 Kinetic Theroy: Molecular explanation of pressure and temperture • -Kinetic theoryexplain pressure and temperture on a submicroscopic view • -Assume elastic collision of gas molecules with the wall of a container • Force on the wall (rate of change of momentum) • Number of molecules ↑, P ↑ • Average velocity ↑, P ↑ See p.306 for derviation

13. 12.4 Kinetic Theroy: Molecular explanation of pressure and temperature • Example 12.8 Energy and Speed of a gas molecule • Average KE of a gas molecule at 200C = ? • rms speed of N2 molecule at 200C = ? • Solutions • (a) =1.5*1.38*10-23*293 = 6.07*10-21 J (b) = 511 m/s Individual molecules do not move very far- sound waves are transmiited at speeds related to the molecular speed Molecules bounce furiously- Billions of collisions per second

14. Distribution of Molecular Speeds, p.308 Maxwell-Boltzmann distribution of molecular speeds in an ideal gas - vp= the most likely speed < vrms - Only a tiny fraction of molecules have very high speeds

15. Distribution of Molecular Speeds, p.308 vp is shifted to higher speeds and is broadened at higher temperature. Total probaility = 1

16. 12.5 Phase Changes (相變) • Real gas – attraction among molecules • Condensing to liquid (Gas  Liquid) • freezing to a solid (Liquid  Solid) • Volume dramatic ↓ Absolute zero

17. 12.5 Phase Changes (相變), PV diagram Hyperbolic shape(雙曲線), isotherms(等溫線) Condensate/Vapourize 雙曲線 Liquid V↓a little, as P↑ Gas V↓a lot, as P↑

18. 12.5 Phase Changes (相變) Critical point TC – above which liquid cannot exist CO2 cannot be liquefied at T > 310C Critical pressure – minimum pressure needed for liquid to exist at TC

19. 12.5 Phase Changes (相變) p.310,Table 12.2 (Critical temp.and pressure),Helium is last liquefied gas • PT graph – Phase diagram for water • solid lines  phase equilibrium • liquid-vapour curve • - boiling point • - critical point • (2)solid-liquidcurve • - melting point (00C at 1 atm) • - at fixed temp., (00C) • ice  water (by↑P) Liquid phase not exist at any P boiling point

20. PT graph – Phase diagram for water • solid-vapour curve • - interesting, at lower pressure, • there is no liquid phase • - exist either as gas or solid • - sublimation(昇華) • - for water this is true for • P > 0.0060 atm • Triple point  all three phases in • equilibrium, at 273.16 K (0.010C) • A more accurate calibration temp. • than melting point ! • p.310, Table 12.3 Triple point

21. p.315 - Phase diagram of CO2

22. Equilibrium between liquid and gas at two different boiling points Equilibrium at lower temperature  Lower rate of condensation and vaporization • Equilibrium at higher temperatur • Higher rate of condensation and vaporization Dynamics equilibrium

23. Vapor pressure, Partial pressure and Dalton’s Law Vapor pressure = the gas pressure created by the liquid or solid phases of a substance Partial pressure = the gas pressure created if it alone occupied the total volume available Dalton’s Law of partial pressures Total pressure = sum of partial pressures of the component gases, Assume ideal gases and no chemical reactions

24. 12.6 Humidity, Evaprotation, and Boiling • p.312, Table 12.4 - Saturated vapor density of water • T ↑  vapor pressure ↑ • Relative humidity– how much water vapor is in the air compare with • the maximum possible. • Relative humidity is related to the partial pressure of water vapor in the air • At 100% humidity (dew point) • partial pressure of water vapor = vapor pressure • partial pressure < vapor pressure  evaporataion (humidity < 100%) • partial pressure > vapor pressure  condensation • Relative humidity, • RH= (vapor density/saturation vapor density)*100%

25. Example 12.10 Density and vapor pressure At T=200C, vapor pressure = 2.33*103N/m2, use ideal gas law to Calculate thedensity of water vapor in g/cm3 that would create a partial pressure = vapor pressure. Solutions PV = nRT  n/V = P/RT P/RT = 2.33*103/8.31/293 = 0.953 mol/m3 The molecular mass of water = 18.0  18.0 g/mol  mass = 18*(number of mole = n)  density = mass/V = 0.953*18 = 17.2 g/m3

26. 12.6 Humidity, Evaprotation, and Boiling • Some water molecules can escape – Maxwell-Boltzmann distribution • Sealed container – evaporation will continue until • evaporation = condensation • Vapor pressure = partial pressure of vapor  Saturation(飽和)

27. 12.6 Humidity, Evaprotation, and Boiling • Example 12.11 Humidity and Dew point • Calculate RH, T=250C, density of water vapor = 9.4 g/m3 • At what T=?, will this air reach 100% RH–dew point • What is the humidity when T=25.00C and the dew point is -10.00C • Solutions • RH = (9.40/23.0)*100% = 40.9% Table 12.4 • From Table 12.4, 9.4 g/m3 RH is 100% at 10.00C • From Table 12.4, at -10.00C, saturated vapor density = 2.36 g/cm3 • RH = (2.36/23.0)*100% = 10.3%

28. 12.6 Humidity, Evaprotation, and Boiling Why does air formed when water boils ? Bubble started at 200C has P = 1 atm As T↑ water vapor enters the bubble, vapor pressure ↑ Bubble expands to keep P = 1 atm As T↑more water vapor enter the bubble  bubble expand Buoyant force on it increase  bubble breaks  boiling

29. Homework, due next week Ch. 11 11.21, 11.29, 11.31, 11.45, 11.53 Ch. 12 12.37, 12.47, 12.57