Temperature and Heat

1
Chapter 15

• Temperature and Heat

2
Mechanics vs. Thermodynamics

• Mechanics
• obeys Newtons Laws
• key conceptsforce kinetic energy static
  equilibriumNewtons 2nd Law

• Thermodynamics
• will find new laws
• key conceptstemperature, heatinternal energy
  thermal equilibrium2nd Law of Thermodynamics

3
Temperature (T)

• Temperature a macroscopic quantity
• (see later T is related to KE of particles)
• many properties of matter vary with T (length,
  volume, pressure of confined gas)

4
Temperature (T)

• Human senses can be deceiving
• On a cold day iron railings feel colder than
  wooden fences, but both have the same T
• How can we define T ?
• Look for macroscopic changes in a system when
  heat is added to it

5
Two Thermometers

• Add heat to (a) and (b).
• (a) liquid thermometer
• liquid level rises
• T is measured by L
• (b) constant volume gas thermometer
• gas pressure p rises
• T is measured by p

6
Using Thermometers

• put the bulb of (a) in contact with a body
• wait until the value of L (i.e. T) settles out
• the thermometer and the body have reached thermal
  equilibrium (they have the same T)

7

• Consider thermal interactions of systems in (a).
• red slab thermal conductor (transmits
  interactions)
• blue slab thermal insulator (blocks
  interactions)

Demonstration
8

• Let A and C reach thermal equilibrium (TATC).
• Let B and C reach thermal equilibrium (TBTC).
• Then are A and B in thermal equilibrium (TATB)?

Demonstration
9

• In (a), are A and B in thermal equilibrium?
• Yes, but its not obvious!
• It must be proved by experiment!

Demonstration
10

• Experimentally, consider going from (a) to (b)
• Thermally couple A to B and thermally decouple C.
• Experiments reveal no macroscopic changes in A, B!

Demonstration
11

• This suggests the Zeroth Law of Thermodynamics
• If C is in thermal equilibrium with both A and
  B,then A and B in thermal equilibrium with each
  other.

Demonstration
12

• This means If two systems A and B are in
  thermal equilibrium, they must have the same
  temperature (TATB), and vice versa

Demonstration
13
Temperature Scales
14
Temperature Scales

• Three scales Fahrenheit, Celsius, Kelvin
• To define a temperature scale, we need one or
  more thermodynamic fixed points
• fixed point a convenient, reproducible
  thermodynamic environment

15
Temperature Scales

• Both Fahrenheit and Celsius scales are defined
  using two fixed points
• freezing point and boiling point of water
• Kelvin scale defined using one fixed point
• triple point of water (all three phases
  coexist ice, liquid, vapor)

16
Temperature Scales Summary

• Relations among temperature scales
• Fahrenheit temperature
• Celsius temperature
• Kelvin temperature

17
Temperature ScalesKelvin vs. Celsius

• triple point of water
• we measure TC, triple 0.01oC
• we define TK, triple 273.16 K
• (DT)K (DT)C so the unit of DT is K or oC
• the scales differ only by an offset, so
  TK TC 273.15

18
Kelvin Temperature Scale

• Fixed point triple point of water TK, triple
• p pressure of ideal (i.e. low density) gas
  (on a constant volume gas thermometer)
  (has value ptriple at TK, triple)
• We define

19

• At low density, see same graph for all gases
• Extrapolate to p0 (at T absolute zero K)

Demonstration
20
Thermal Expansion
21
Thermal Expansion

• Empirical law for solids, valid for small DT
• (simple case all directions expand equally)
• For a gt 0
• If DT gt 0 DL gt 0 , material expands
• If DT lt 0 DL lt 0 , material compresses

22
Thermal Expansion

• a coefficient of linear expansion gt 0
  (almost always)
• characterizes thermal properties of matter
• varies with material (and range of T)
• unit 1/K, or 1/oC since (DT)K (DT)C

23
Thermal Expansion

• Example two different materials have different
  DL
• They can be used to build a thermometer or a
  thermostat

24

• Atomic explanation of thermal expansion!
• Recall spring model for diatomic molecule
• Van der Waals potential energy, U

Demonstration
25
Thermal Expansion

• Similar for a solid made of many atoms
• Each pair of atoms has a potential energy U
• The asymmetry of U explains thermal linear
  expansion!

26
Thermal Volume ExpansionSolids and Liquids

• b coefficient of volume expansion
• varies with material (and range of T)
• unit 1/K, or 1/oC since (DT)K (DT)C

27
Thermal Volume ExpansionSolids

• Find a simple relationship between linear and
  volume expansion coefficients
• b 3a

28
Thermal Expansion of Water

• unusual state
• a lt 0 if0o C lt T lt 4o C
• (its why lakes freeze from the top down)

29
Thermal Stress

• Thermal stress stress required to counteract
  (balance) thermal expansion
• Tensile thermal stress

30
Announcements

• Midtermswill probably be returned Monday
• Homework 5 is returned at front
• Homework Extra Credit is on record (but not yet
  listed on classweb if it brings a score over the
  maximum)

31
Temperature ScalesKelvin vs. Celsius

• triple point of water
• we measure TC, triple 0.01oC
• we define TK, triple 273.16 K
• (DT)K (DT)C so the unit of DT is K or oC
• the scales differ only by an offset, so
  TK TC 273.15

32
Heat and Heat Transfer
33
Quantity of Heat (Q)

• Heat energy absorbed or lost by a body
  due to a temperature difference
• Heat energy in transit
• SI unit J
• other units 1 cal 4.186 J
  1 kcal calorie on food labels

34
Quantity of Heat (Q)

• Q gt 0 heat is absorbed by a body
• Q lt 0 heat leaves a body
• (we will see several expressions for Q)

35
Quantity of Heat (Q)

• Conservation of energy (calorimetry)
• For an isolated system, the algebraic sum of all
  heat exchanges add to zero
• Q1 Q2 Q3 ... 0

36
Absorption of Heat

• Q heat energy required to change the
  temperature of material (mass m) by DT
• c specific heat capacity of the material
  (treat as independent T) unit J/(kg
  K)

37
Absorption of Heat

• If Q and DT positive heat absorbed by m
• If Q and DT negative heat leaves m

Do Exercise 15-35
38
Phase Changes

• phase state of matter solid,
  liquid, vapor
• energy is needed to change phase of matter
• under a phase transition of matteronly its
  phase changes, not its temperature!

39
Phase Changes in Water
40
Solid-Liquid Phase Change Q mLf

• mLf heat needed for phase change
• Lf (latent) heat of fusion of the material
  (heat/unit mass) needed for transition
  unit J/kg
• for melting (solid to liquid) for freezing
  (liquid to solid)

Do Exercise 15-51
41
Liquid-Vapor Phase Change Q mLv

• mLv heat needed for phase change
• Lv (latent) heat of vaporization
  (heat/unit mass) needed for transition
  unit J/kg
• for evaporating (liquid to vapor) for
  condensing (vapor to liquid)

42
Heat Transfer
43
Heat Transfer

• dQ/dt rate of heat flow
  heat current
• Three mechanisms for achieving heat transfer
• Conduction
• Convection
• Radiation

44
Heat Transfer Mechanisms

• Conduction Collisions of molecules, no bulk
  motion
• ConvectionBulk motion from one region to
  another
• RadiationEmission of electromagnetic waves

45
Conduction
46
Conduction

• k thermal conductivity of material unit
  W/(mK)
• A cross sectional area of material
• L length of material

47
Conduction
Do Exercises 15-57, 15-58
Notes on a composite conducting rod
48
Convection (usually complicated)
49
Radiation (e.g. emitted by the sun)
50
Radiation Electromagnetic Waves
51
Emission of Radiation

• all bodies emit electromagnetic radiation
• A surface area of body
• T surface temperature of body
• e emissivity of body (0 lt e lt 1)

Do Exercise 15-67
52
Absorption of Radiation
Example of net radiation and Problem 15-89

• In general, bodies emit radiation and also absorb
  radiation from their surroundings
• T surface temperature of body
• TS surface temperature of surroundings