Temperature, States of Matter, and Physics

1
Temperature, States of Matter, and Physics

• Temperature is due to Kinetic Energy of Particles
• Translational ½ mv2 linear motion
• Rotational ½ Iw2 Spinning motion
• Vibrational ½ kx2 Spring motion
• In solids, vibrational rules not enough to
  cause separation of particles
• In liquids, all three apply, but not enough to
  cause disruption of intermolecular forces
• In gases, linear rules particles fly about
  freely

2
Thermometers and Thermal Equilibrium

• Thermometers work by quickly getting to the same
  temperature as its surroundings
• Thermal equilibrium is reached between two
  objects when they have no difference in
  temperature

3
Thermometry

• Scales of measurement
• Celsius based on boiling and freezing of water
  100 boiling 0 Freezing
• Fahrenheit based on body temperature and
  freezing point of salt-water mixture
• Conversion between
• C 5/9 ( F 32 ) or F 1.8C
  32
• Kelvin or Absolute based on relation of volume
  to temperature in gases. By extrapolation,
• Ø K -273.15C

4
Temperature

• Temperature Is Not Heat
• Temperature measures average energy of one
  molecule
• Heat measures total energy of all molecules
  present

5
Thermal Expansion

• As object gains heat, molecules move farther
  apart
• Expansion vs. contraction
• Must be accounted for in these cases
• a. Dentistry
• b. Car engines vs piston
• c. Bridges and roadways

6
Thermal Expansion

• Rates different for different materials
• Bimetallic strips-- connection of two strips with
  different coefficients of expansion
• Motion caused by side with greater expansion or
  contraction
• Thermostats use this to act as a switch
• Pyrex glass made to limit expansion
• Liquids expand more than solids
• Gases expand/contract more than either solid or
  liquid

7
Thermal expansion

• When substances are heated, they expand Linear
  and Volume expansion take place
• Linear Change in length is proportional to
  original length and change of temperature
• ?L L0?? T ? coefficient of linear
  expansion
• New length equation L L0( 1 ? ?T )

8
Examples 11.3 11.4

• The Verrazano-Narrows Bridge has a center span of
  1300 m. Allowance has been made for thermal
  expansion and contraction of its materials, and
  the bridge is steel, so, for safety, allowing for
  a temperature range of 120C, how much thermal
  expansion must be allowed for in the center span?
  
• Obtain the change in length of the center span
  from the definition of thermal expansion
• ?L L0 ??T
• ? L (1300m)(12 x 10-6 C-1)(120C) 1.9 m.
• The total allowance for expansion must be 1.9 m.
• A copper hot-water pipe is 10.0 m long when cut
  and installed in a building on a day when the
  temperature is 10C. How long is the pipe when
  it carries hot water at 60C if the pipe is free
  to expand?
• Use the equation
• L L01 a(T T0)
• L (10.0 m)1 (17 10-6 C-1)(60C - 10C)
• L (10.0 m)(1.00085) 10.0085 m 1000.85 cm.

9
Thermal Expansion

• Area and Volume Same relation as length
• Equations ? A A0g ? T
• ? V V0b ? T
• Gases expand most, liquids and solids much less
  see table of a and b p. 319

10
Example 11.5

• A 1.00-liter glass bottle is filled to the brim
  with water at a room temperature of 20C. The
  temperature of the bottle and the water is then
  raised to 95C. Does the water spill over, or
  does the level go down, and by how much?
• Because the volume coefficient of thermal
  expansion of water changes with temperature, use
  the average value of
• b 525 10-6 C for the range of 20C to
  95C.
• Write the change in volume ? Vglass for the
  bottle as
• ? Vglass V0b ? T
• ? Vglass (27 10-6 C-1)(1.00 10-3
  m3)(95C - 20C) 2.03 cm3
• For the water the change in volume ? Vwater is
  ? Vwater V0b ? T
• ? Vwater (525 10-6 C-1)(1.00 10-3
  m3)(95C - 20C) 39.4 cm3
• The expansion of the water is greater than the
  expansion of the bottle. The amount of water
  that will run over the edge is
• ? Vwater ?Vglass 39.4 cm3 2.03 cm3 37.4
  cm3

11
Water The Exception

• Water expands from 4C both heating and cooling.
• Ice is much less dense than liquid water.
• Water freezes from top downward.
• Lakes even in very cold climates never freeze
  totally.

12
Water The Exception

• Specific heat capacity is quite high
• Takes long to heat or to cool
• Cause moderation of climate of areas near large
  bodies of water

13
Homework 1

• p335ff 2, 3, 9, 10, 19

14
Gases and Physics

• Gases exert force on surfaces due to collision of
  their particles
• This is translated into Pressure (force per unit
  area), P F/A
• Units of pressure are N/M2 or Pascals
• Atmospheric gases exert pressure on everything
  around due to the weight and density of air at
  the surface

15
Gas Laws

• Robert Boyle discovered by experiments that
  volume of a contained gas was inversely
  proportional to its pressure
• Charles and Gay-Lussac likewise discovered that
  temperature was directly proportional to both
  volume and pressure
• These led to the ideal gas law

16
Ideal Gas Law

• Combination of other laws involving moles,
  volume, temperature, and pressure
• Involves R, the universal gas constant has
  variable units, depending on usage.
• In physics, we use 8.31 J/mol x K
• Equation PVnRT
• For changing conditionsEquation
• P1V1T2 P2V2T1

17
Ideal Gas Law

• Combination of other laws involving moles,
  volume, temperature, and pressure
• Involves R, the universal gas constant has
  variable units, depending on usage.
• In physics, we use 8.31 J/mol x K
• Equation PVnRT
• For changing conditionsEquation
• P1V1T2 P2V2T1

18
Kinetic Theory of Gases

• Same as in Chemistry, applies to ideal gases
• 1. Gases consist of many tiny particles
• 2. Volume of the particles is negligible
  compared to that of their container
• 3. Direction and speed of particles is entirely
  random
• 4. Collisions are perfectly elastic with no
  attraction between particles
• 5. Molecules obey Newtons laws of motion.
• These apply generally but not perfectly to real
  gases

19
Kinetic Theory and Kinetic Energy

• By manipulation the Ideal Gas Law becomes
• PV 2/3(N KE) where N is the number of
  individual gas particles
• Rearranging and involving the temperature
• KE 3/2 kT where k 1.38 x 10-23 J/K
• or T2/3 KE/ k

20
Homework 2

• p337ff
• 25, 33, 36, 37, 39

21
Mechanical Equivalent of Heat

• Heat was thought to be a substance, caloric.
• Demonstrated by Count Rumford that heat happens
  due to work.
• Quantitatively demonstrated by James Prescott
  Joule with special apparatus
• Heat energy measured in both Joules and calories
  calorie amount of heat to raise 1g of water
  by 1C.
• 1cal 4.187 Joules

22
Example 11.6

• A 1500-W heater is submerged into one kilogram of
  water that is well below 100C. At what rate, in
  C/s, does the temperature rise when the heater
  is operating at its rated power?
• The rate of energy input is
• 1500 J/s 1 cal 358.3 cal/s
• 4.187 J
• The rate of energy input per gram is
• 358.3 cal/s 0.358 cal/g s.
• 1000 g
• Since each gram of water receives 0.358 cal/s,
  the temperature of each gram of water, and
  therefore the entire volume of water, increases
  by 0.358C/s.

23
Calorimetry

• The measurement of heat exchanged.
• Depends on mass and ability to transfer heat or
  heat capacity.
• Q mc?T
• Q heat transferred
• C heat capacity

24
Examples 11.7

• A Styrofoam cup of negligible heat capacity
  contains 150 g of water at 10C. If 100 g of
  water at a temperature of 85C is added, what is
  the final temperature of the mixture after it has
  been thoroughly mixed?
• The heat gained by the cooler water is
• Qgain m1c ? T1 m1c(T T1,0) (150 g)c(T -
  10C).
• The heat lost by the hotter water is
• Qlost m2c ? T2 m2c(T T2,0) (100 g)c(T -
  85C).
• When the heat lost plus the heat gained is set
  equal to zero, the resulting expression
  determines a unique value for the final
  temperature T
• Qlost Qgain 150c(T-10) 100c(T-85) 0
• (150100)T (8500 1500) T 40C

25
Example 11.8

• A metal block of 74 g heated in an oven to 90 C
  is placed in a calorimeter with 300 g water at
  10C. If the final temperature is 14C, is the
  block Al, Fe, Ag, or Zn?
• Qlost mc?T (0.074)c(14-90) -5.62c
• Qgain (0.300)(4187)(14-10) 5024 J
• Qlost Qgain -5.62c 5024 0
• 5.62c 5024
• c 894 J/kg C nearly the c of Al

26
Phase Change and Energy

• Phase change requires energy to break
  intermolecular forces
• Energy required is heat of transformation
• Transformation can be either at melting or
  boiling point.
• L Q/m or Q mL
• Heat of fusion at melting point Lf
• Heat of vaporization at boiling point Lv

27
Example 11.9

• A 105-g copper calorimeter contains 307 g of
  water at room temperature (T 23ºC). If 52 g of
  ice at 0ºC is added to the colorimeter, what is
  the final temperature of the system?
• Qgain miceLf micecwater?T
• (52 g)(80 cal/g) (52 g)(1 cal/g
  ºC)(T-0 ºC)
• 4160 cal 52T cal/ºC
• Qlost mwcw?T mccc?T (mwcw mccc)(T - T0)
• (307 g)(1 cal/g ºC) (105 g)(0.092
  cal/g ºC)(T-23ºC)
• (317 cal/ ºC)(T-23 ºC)
• 317T cal/ ºC 7290 cal
• Add heat gain to heat lost
• 4160 cal 52T cal/ ºC 317T cal/ ºC 7290 cal
  0
• 369T cal/ ºC 3130 cal
• T 8.5 ºC

28
Homework 3

• p363ff
• 5, 7, 11, 15, 22, 29

29
Heat Transfer

• Heat moves by three main methods
• Conduction heat movement by direct contact of
  items usually involved with solids
• Convection heat movement in fluids, where
  transfer is due to fluid movement
• Radiation heat movement by waves from
  electromagnetic sources

30
Conduction

• Happens between materials in direct contact
• Due to collisions of atoms or molecules and
  electrons
• Conduction accounts for cooler feel of metals vs.
  nonmetals
• Good conduction feels cool
• Insulators, poor conductors delay
• heat transfer
• Liquids and gases usually poor conductors/good
  insulators
• Cold is not transferred

31
Conductivity

• Through solids, heat conductivity is controlled
  by area, thickness, and temperature difference
• The rate of heat flow is calculated by
• ?Q/?t K A ?T /L
• L is thickness
• A is area
• K is thermal conductivity
• High values of K mean good heat conduction, low
  values mean good insulator.

32
Example 11.11

• A Styrofoam cooler has surface area of 0.50 m2
  and an avg. thickness of 2.0 cm. How long will
  it take for 1.5 kg of ice to melt in cooler if
  outside temperature is 30ºC? (thermal
  conductivity of Styrofoam used to make cooler is
  0.030 W/m ºC)
• ?Q/?T KA(T2 T1)/L
• (0.030 W/m ºC)(0.50 m2)(30 ºC - 0
  ºC)/0.020 m 22.5 W
• Heat of fusion of ice Lf 3.34 105 J/kg
• ?Q/?t ?m Lf/?t
• ?t ?m Lf/ (?Q/ ?t)
• (1.5 kg)(3.34 105 J/kg)/22.5 W
• 2.23 104 s
• convert to hours ?t 6.2 hours for all ice to
  melt

33
Insulation

• Home insulation limits heat flow and is measured
  accordingly
• R-values listed in hardware stores tell
  effectiveness
• R L/K

34
Radiation

• Heat due to energy waves passing thru space
• From electromagnetic waves of long wavelength
• Light also from objects emitting heat
• Absorption and Emission of Radiation
• Absorbers of radiation appear black
• Good absorbers also are good emitters--thermal
  equilibrium requires it

35
Radiation

• Hot objects lose energy by radiation
• Black objects fastest, silvered objects slowest
• Radiated power in watts calculated by
• P ?eAT4 ? StefanBoltzmann constant (5.67
  10-8)
• e emissivity constant for material
• A area of surface
• Objects lose energy compared to their
  surroundings so this must be rewritten to
• Pnet ? eA(T4-Ts4)

36
Example 11.12

• A patient waiting to be seen by his physician is
  asked to remove all his clothes in an examination
  room that is at 16C. Calculate the rate of heat
  loss by radiation from the patient, given that
  his skin temperature is 34C and his surface area
  is 1.6m2. Assume an emissivity of 0.80.
• Solution The rate of heat loss by radiation is
• Pnet ?eA (T4 - T4s),
• Where the temperature is expressed in kelvins.
  Inserting the numbers, we get
• Pnet (5.67 x 10-8 W x m-2 x K-4)(0.80)(1.6 m2)
  (307 K)4 (289 K)4
• Pnet 140 W.

37
Homework 4
31, 35, 37, 56
38
New Equations!!

• CK-273.15 KC273.15 F9/5C 32
• DLaL0DT DAgA0DT DVbV0DT
• PVnRT 1/2mvrms23/2kBT
• vrmsv(3RT/M) QmcDT QmLv or mLf
• HcondQ/Dt kA (DT/L)
• Prad sAeT4