Chapter 12 Temperture, Kinetic Theory, and the Gas Law
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Transcript of Chapter 12 Temperture, Kinetic Theory, and the Gas Law
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Chapter 12Temperture, Kinetic Theory, and the
Gas Law
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12.1 Temperature
Operational - measured by thermometer,using physical properties of materials, such asvolume change, resistance change and color change
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Relation among Fahrenheit, Celsius, and Kelvin temperture scales.
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Logarithmic scale of tremendous range of tempertures in nature.
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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
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This crack in a concrete sidewalk was created by thermal stress,an indication of how great such stress can be.
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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
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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 ↑
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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
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NA = 6.02*1023 /mol Macroscopic like this mole of table tennis balls covering theEarth to a depth of about 35 km !
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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
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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
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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
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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
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Distribution of Molecular Speeds, p.308
vp is shifted to higher speeds and is broadened at higher temperature.
Total probaility = 1
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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
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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
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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
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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
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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
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p.315 - Phase diagram of CO2
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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
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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
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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%
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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
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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 )
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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%
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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
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Homework, due next week
Ch. 11 11.21, 11.29, 11.31, 11.45, 11.53 Ch. 12 12.37, 12.47, 12.57
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