Physics 13: Temperature and Kinetic Theory

1
Physics 13 Temperature and Kinetic Theory

• Christopher Chui

2
Atomic Theory of Matter

• Dalton (1800s) law of definite proportions
• Atomic mass assign C12.0000 u
• 1 u 1.66 x 10-27 kg
• Molecular mass sum of all atomic masses in 1
  molecule of compound
• Brown (1927) atoms are constantly in motion
• Molecular motion stops at unreachable 0o K
• Diameter of a typical atom 10-10 m

3
Temperature and Thermometers

• Temperature is a measure of hot/cold
• Thermometers are instruments to measure
  temperature
• In science, both Celsius and Kelvin are used
• Fahrenheit scale is used in daily lives
• Water freezes at 0o C or 32o F or 273o K at 1 atm
• Water boils at 100o C or 212o F or 373o K at 1
  atm
• 2 simple formulas C 5/9 F-32 F 9/5 C
  32
• Constant-volume gas thermometer is chosen as the
  standard thermometer

4
0th Law of Thermo Expansion

• If 2 systems are in thermal equilibrium with a
  3rd system, then they are in thermal equilibrium
  with each other
• Linear expansion DL aL0 DT L L0 (1 a DT)
• Coefficient of vol expansion 3 x coeff of
  linear exp
• Volume expansion DV bV0 DT
• Water is unusual it expands when cooled from 4o
  C to 0o C. For this reason, life exists under ice

5
Thermal Stresses Gas Laws

• Large stress exists for expansion
• DL 1/E F/A L0 ? aL0 DT 1/E F/A L0 ?F aEADT
• Boyles law (1600s) the volume of a gas is
  inversely proportional to the pressure applied to
  it when the temperature is kept constant ? V prop
  1/P
• PV constant when T is kept constant
• Absolute zero -273.15o C 0o K K C 273.15
• Charles law the volume of a given amount of gas
  is directly proportional to the absolute
  temperature when the pressure is kept constant ?
  V prop T
• Gay-Lussacs law at constant volume, the
  pressure of a gas is directly proportional to the
  absolute temperature ? P prop T
• Ideal gas law PV prop T or PV prop mT PV nRT

6
STP and Avogadros Number

• STP (standard temp and pressure) 273K and 1 atm
• Under conditions 1 and 2 P1V1/T1 P2V2/T2
• 1 mole of gas at STP has volume 22.4 L
• Always give T in K, and P as absolute, not gauge,
  P
• Equal volumes of gas at the same pressure and
  temperature contain equal numbers of molecules
• Avogadros number 6.02 x 1023
• Ideal gas law PV NkT in terms of no. of
  molecules
• Boltzmanns constant, k R/NA 1.38 x 10-23 J/K

7
Kinetic Theory of Molecules

• 1. Large number of molecules, N, each of mass m,
  move in random directions with a variety of
  speeds
• 2. Molecules are far apart from one another
• 3. Molecules are assumed to obey the laws of
  classical mechanics and assumed to interact when
  they collide
• 4. Collisions with another molecule or the wall
  of the vessel are assumed to be perfectly elastic
• All gas laws can be explained using the kinetic
  theory of gases

8
Kinetic Energy of Gases-1

• Pressure in a gas 1/3 NmV2 / V
• Average KE ½ mv2 3/2 kT
• The average translational kinetic energy of
  molecules in a gas in directly proportional to
  the absolute temperature
• Root-mean-square (rms) velocity sq v2sq(3kT/m)
• Maxwell distribution of speeds skewed normal
• Activation energy, EA, is the min energy required
  for a chemical reaction to occur
• For real gases, there is a critical temperature
  at which liquid and gas coexist at the same time
• On a P vs T graph (phase diagram), a triple point
  exists at which solid, liquid, and gas coexist
  together

9
Kinetic Energy of Gases-2

• Kinetic theory predicts that evaporation is a
  cooling process. Fast moving molecules evaporate.
  Some molecules strike the liquid surface and
  condense
• The pressure of the vapor when it is saturated is
  the saturated vapor pressure
• Vapor pressures occur at all temperature above 0
  K
• When temperature is raised above the vapor
  pressure, boiling occurs. At boiling, saturated
  vapor pressure external pressure
• The total pressure is the sum of all partial
  pressures of each gas present

10
Kinetic Energy of Gases-3

• Partial pressure is the pressure each gas would
  exert if it were to occupy the whole volume
• Relative humidity is the ratio of the partial
  pressure to the saturated vapor pressure at a
  given temp.
• Relative humidity partial pressure of H2O /
  saturated pressure of H2O 100
• Proper humidity is maintained in museums to
  protect artwork. A humidity of 40-50 is optimum
  for comfort
• If the partial pressure of water gt the saturated
  vapor pressure, the air is supersaturated
• When air containing water is cooled, a
  temperature is reached where the partial
  pressuresat vapor pressure?dew point

11
Diffusion

• Random movement of foreign molecules throughout a
  liquid or gas is called diffusion
• The diffusing substance moves from a region where
  its concentration is high to one where its
  concentration is low
• Concentration gradient (C1 C2)/Dx
• Ficks law rate of diffusion, J DA(C1 C2)/Dx
• D is the diffusion constant
• Diffusion occurs in plants and animals for
  nutrients and gases