Chapter 12Temperture, Kinetic Theory, and the

Gas Law

12.1 Temperature

Operational - measured by thermometer,using physical properties of materials, such asvolume change, resistance change and color change

Relation among Fahrenheit, Celsius, and Kelvin temperture scales.

Logarithmic scale of tremendous range of tempertures in nature.

12.2 Thermal expansion of solids and liquids

p.299 Table 12.1, coefficient of linear and volume(~3*linear) expansionObjects expand in all directions as temperature incresass. (a) Area increases(b) Size of the hole increases(c) Volume increase

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

12.3 The Ideal Gas Law

Ideal gas no attraction among gas molecules

PV = NkT

P = pressure of gas , V = volume of gasT =temperature (K) N= number of atoms or molecules in the gask = 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

When air is pumped into a deflated tire,its volume increased without pressure change

To a certain point, the tire wall resist further expansionand P ↑ with more air.

Once the tire is inflated, P ↑ as T ↑

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?SolutionsGiven 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

NA = 6.02*1023 /mol Macroscopic like this mole of table tennis balls covering theEarth to a depth of about 35 km !

The Ideal Gas Law Restated using Mole

nRTPV

kNR

kTNN

NPV

NkTPV

A

AA

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

12.4 Kinetic Theroy: Molecular explanation of pressure and temperture

-Kinetic theoryexplain pressure and temperture on a submicroscopic view-Assume elastic collision of gas molecules with the wall of a containerForce on the wall (rate of change of momentum)Number of molecules ↑, P ↑ Average velocity ↑, P ↑

m

kTvv

kTvmEK

NkTvm

NkTPV

vNmPV

rms

3

2

3

2

13

1

3

1

2

2

2

2222

ZYX vvvv

See p.306 for derviation

12.4 Kinetic Theroy: Molecular explanation of pressure and temperature

Example 12.8 Energy and Speed of a gas molecule(a) Average KE of a gas molecule at 200C = ?(b) rms speed of N2 molecule at 200C = ?Solutions(a) kTvmEK

2

3

2

1 2 =1.5*1.38*10-23*293 = 6.07*10-21 J

(b) 26

23

10*65.4

293*10*38.1(33

m

kTvrms = 511 m/s

Molecules bounce furiously-Billions of collisions per second

Individual molecules do not move very far- sound waves are transmiitedat speeds related to the molecular speed

Distribution of Molecular Speeds, p.308Maxwell-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

Distribution of Molecular Speeds, p.308

vp is shifted to higher speeds and is broadened at higher temperature.

Total probaility = 1

12.5 Phase Changes (相變 )

Real gas – attraction among moleculesCondensing to liquid (Gas Liquid)freezing to a solid (Liquid Solid) Volume dramatic ↓

Absolute zero

12.5 Phase Changes (相變 ), PV diagram

LiquidV↓ a little, as P↑

GasV↓ a lot, as P↑

Condensate/Vapourize

Hyperbolic shape(雙曲線 ), isotherms(等溫線 )

雙曲線

12.5 Phase Changes (相變 )Critical point TC – above which liquid cannot existCO2 cannot be liquefied at T > 310CCritical pressure – minimum pressure needed for liquid to exist at TC

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 watersolid lines phase equilibrium

(1) liquid-vapour curve - boiling point - critical point(2) solid-liquid curve - melting point (00C at 1 atm) - at fixed temp., (00C) ice water (by↑P)

boiling point

Liquid phase not existat any P

PT graph – Phase diagram for water

(3) 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 atmTriple point all three phases inequilibrium, at 273.16 K (0.010C)

A more accurate calibration temp.than melting point !

p.310, Table 12.3 Triple point

p.315 - Phase diagram of CO2

Equilibrium between liquid and gas at two different boiling points

Equilibrium at lower temperature Lower rate of condensation andvaporization Equilibrium at higher temperatur

Higher rate of condensation andvaporization

Dynamicsequilibrium

Vapor pressure, Partial pressure and Dalton’s Law

Vapor pressure = the gas pressure created by the liquid or solid phasesof a substance

Partial pressure = the gas pressure created if it alone occupied the totalvolume available

Dalton’s Law of partial pressures

Total pressure = sum of partial pressures of the component gases, Assume ideal gases and no chemical reactions

gasesi

ipressurepartialpressuretotal

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 withthe 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%

Example 12.10 Density and vapor pressure

At T=200C, vapor pressure = 2.33*103N/m2, use ideal gas law toCalculate the density of water vapor in g/cm3 that would create a partial pressure = vapor pressure.SolutionsPV = 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

12.6 Humidity, Evaprotation, and Boiling

(a) Some water molecules can escape – Maxwell-Boltzmann distribution(b) Sealed container – evaporation will continue until evaporation = condensationVapor pressure = partial pressure of vapor Saturation(飽和 )

12.6 Humidity, Evaprotation, and Boiling

Example 12.11 Humidity and Dew point(a) Calculate RH, T=250C, density of water vapor = 9.4 g/m3

(b) At what T=?, will this air reach 100% RH – dew point(c) What is the humidity when T=25.00C and the dew point is -10.00CSolutions(a) RH = (9.40/23.0)*100% = 40.9% Table 12.4(b) From Table 12.4, 9.4 g/m3 RH is 100% at 10.00C(c) From Table 12.4, at -10.00C, saturated vapor density = 2.36 g/cm3

RH = (2.36/23.0)*100% = 10.3%

12.6 Humidity, Evaprotation, and Boiling

Why does air formed when water boils ?Bubble started at 200C has P = 1 atmAs T↑ water vapor enters the bubble, vapor pressure ↑ Bubble expands to keep P = 1 atmAs T↑more water vapor enter the bubble bubble expand Buoyant force on it increase bubble breaks boiling

Homework, due next week

Ch. 11 11.21, 11.29, 11.31, 11.45, 11.53 Ch. 12 12.37, 12.47, 12.57