Chapter 16: Temperature and Heat

1
Chapter 16 Temperature and Heat

• Temperature is a fundamental quantity which
  characterizes the physical state of a substance.
  In the microscopic statistical theory, we
  understand temperature as the average energy per
  degree of freedom of motion of the substance.
• Heat is an interaction between two objects,
  particularly the flow of energy from one object
  to another.
• When two objects are placed in thermal contact
  (so that heat is able to flow from one to the
  other), heat will flow until the temperatures of
  the two objects are the same. Then the two
  objects are in thermal equilibrium.

2
Temperature Scales

• Celsius water freezes at 0 C and boils at 100
  C
• Fahrenheit water freezes at 32 F and boils at
  212 F
• Kelvin - water freezes at 273.15 K and boils at
  373.15 K.
• But how do we determine the equal divisions
  between these calibration points?
• Absolute Zero the lowest possible temperature
  0 K 273.15 C
• TK TC 273.15

3
Thermal Expansion

• Most substances expand when heated. They expand
  in all dimensions
• Conceptual Checkpoint 16-3 A washer has a hole
  in the middle. As the washer is heated does the
  hole (a) expand, (b) shrink, or (c) stay the same?

Hint, what happens to the piece cut out to make
the hole?
4
Water is special!
Water is an exception to the rule. Between 0 and
4 C it contracts. Above 4 C it expands. Water
is most dense at 4 C. Precurser to fact that ice
floats! (most solids sink in their own liquid)
Thermal Expansion.
5
Thermometers Thermostats

• Use the expansion of Hg to define a temperature
  scale.
• Use the differential expansion of two dissimilar
  metals to make either a thermometer or a
  thermostat (temperature activated switch)

6
Thermal Expansion Coefficient

• Any linear dimension L of a solid object with
  expand (or contract) with temperature changes.
• If L is the length at temperature T0, then
• L(T0 DT) L DL
• DL a L DT
• (DL/L) a DT
• a is the coefficient of linear expansion
• a itself can be a function of temperature
• a(water) lt 0 for 0º C lt T lt 4º C
• a(Cu) 1710-6 / (º C)
• 1degree Celsius change causes a fractional
  expansion of 17 parts per million.

7
Thermometers Thermostats

• Use the expansion of Hg to define a temperature
  scale.
• Use the differential expansion of two dissimilar
  metals to make either a thermometer or a
  thermostat (temperature activated switch)
• s0 unheated common length
• R radius of curvature of heated metal A
• s Rq heated length of metal A
• Rdr radius of curvature of heated metal B
• sds (Rdr)q length of heated metal B
• ds q dr s0(1aBDT) - s0(1aADT)
• ds s0 ( aB - aA )DT
• ds differential thermal expansion of metals A
  B.

8
Absolute Zero

• Ideal Gas Law (Chapter 17)
• Constant Volume Gas-Thermometer.
• Keep the reference level fixed fixed gas
  volume.
• Adjust height as temperature of gas is varied
• Pressure of gas r g h
• Pressure curves extrapolate to a common zero
  pressure at a common temperature
• T -273.15 C -460F

http//jersey.uoregon.edu/vlab/Piston/
9
http//chemed.chem.purdue.edu/genchem/topicreview/
bp/ch4/gaslaws3.html
H2 N2 at 0deg C CO2 at 40deg C
http//chemed.chem.purdue.edu/genchem/topicreview/
bp/ch4/deviation5.html
10
Heat
Heat Q is the energy transferred between one
object and another due to temperature
differences. Heat is measured in calories
(cal). 1 cal 4.186 J A Calorie (C) is a
kilocalorie. Salad oil 8.6kC / kg ? 8.6 kC
/litre36106 J/litre Gasoline has only slightly
greater energy density Mechanical energy can be
converted into heat. Examples?
11
Solar Energy Agriculture

• The solar flux is 1 kW/m2.
• The atmosphere absorbs about ½, we lose ½ for
  night time, the growing season is ½ the year, ½
  the days are cloudy.
• Modern agriculture is about 3 efficient at
  turning solar energy into plant chemical energy.
  Assume ¼ of this can be recovered in a seed oil
  (sunflower, etc), convertible to diesel.
• Total yield of 1 hectare 100m x 100 m
• (1000 W/m2) (104 m2) (1/2)4 (0.03) (1/4) ? 1
  Cal/s
• Gasoline consumption 1 gallon/person/day
• 1 gallon oil/day ? 34,000 Cal/day 0.4 Cal/s
• We could power all of our vehicles on bio-diesel,
  
• But modern agriculture uses 1 gallon of fossil
  fuel to make 1 gallon of bio-diesel.
• Need a non-fossil fuel dependent agriculture.

12
Specific Heat

• If you add heat to a substance its temperature
  will increase. But how much? That depends on
  the specific heat of the substance.
• Q mcDT
• Q heat added
• m mass
• c specific heat
• DT change in temperature
• Water has a very large heat capacity a lot of
  energy transfer (heat) is required to change its
  temperature. This has a major impact on the
  climate.
• Water c 1.0 cal /(ºC g) 1.0 Cal /(ºC kg)
• It takes one calorie to raise the temperature of
  1 gm of water by 1 degree Celsius (use this to
  define 1 calorie).

13
Mechanical Equivalent of Heat

• Conservation of energy can be broadened to
  include thermal energy
• Work done on system by non-conservative forces
  heat thermal energy added to system
• Rub your hands to warm them (work done by
  friction).
• 1 calorie 4.18 Joule

14
Specific Heat, values

• Table 16-2

15
Walker Problem 29, pg 530
1.0-g lead pellets at 75 C are to be added to
180 g of water at 22 C. How many pellets are
needed to increase the equilibrium temperature to
25 C?
16
Conduction

• There are three ways in which heat can be
  transferred from one object to another
• Conduction when two objects are in physical
  contact.

k thermal conductivity Q heat transferred A
cross sectional area t duration of
heat transfer L length
DT temperature difference between two ends
In a hot oven the air and the metal rack are at
the same temperature, but which one feels hotter
and why?
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Thermal Conductivities, Table 16-3

• Metals have high thermal conductivity, most
  electrical insulators also have low thermal
  conductivity.
• Air is a great insulator, except that large air
  spaces allow heat flow by convection.

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Convection and Radiation

• Convection when heat is carried by a moving
  fluid
• Heat house with radiator
• Gulf stream transports Heat from Caribbean to
  Europe
• Cold air inside window (in winter) sinks, creates
  convection cold draft
• Radiation when electromagnetic waves
  (radiation) carry heat from one object to
  another.
• Example heat you feel when you are near a fire
• Example Heat from the sun
• Formation of frost (ice) at night,
• T(air) gt 0ºC, but surface temp drops below 0ºC.

19
Black Body Radiation

• Any object heated to a temperature T (on an
  absolute scale) radiates Electromagnetic Energy
  (light) with total power
• P e s A T4
• 0ltelt1 emissivity property of material
• s 5.67 10 8 W/(m2 K4)
• A surface area of object
• Peak wavelength occurs at l (5.110-3 m K ) /
  T (Chap 30)
• Early triumph of quantum theory (M. Planck) to
  predict Power and wavelength equations, including
  the values of the constants, with just one free
  parameter (now called Plancks constant).
• If the surroundings have temperature TS, then the
  net power radiated is
• P e s A T4 - TS4
• Dark, dry, night, TS 3 K, Black body radiation
  cools the surface faster than conduction can
  transport heat from the ground or air. Frost can
  form even if air temperature gt 0C.

20
Linear Dimension Area

• A disk has radius r. Which is true
• The circumference of the disk is 2pr and the area
  is pr2
• The circumference of the disk is pr2 and the area
  is 2pr

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Thermal Expansion

• A metal disk of radius r 5.00 cm and thickness
  d1.00mm is heated such that every linear
  dimension expands to 1.001 times its original
  length.

• What is the fractional change fC(2pr)/(2pr) in
  the circumference of the disk?
• 0.999
• 1.000001
• 1.001
• 1.002001?1.002

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Thermal Expansion

• A metal disk of radius r 5.00 cm and thickness
  d1.00mm is heated such that every linear
  dimension expands to 1.001 times its original
  length.

• What is the fractional change fA(pr2)/(pr2) in
  the area of the disk?
• 0.999
• 1.000001
• 1.001
• 1.002001?1.002