1. Temperature and Heat (Chapter 12)
What is temperature?
- Is there a difference between heat and temperature?
- What does it mean to say something is hot or cold?
Temperature of a body is a measure of the average kinetic energy of its constituent atoms.
Unlike heat (called thermal energy) temperature of a substance is not dependent on the type and number of atoms present (i.e. mass).
How can we define “hot” or “cold”?
Senses – Touch: can be very misleading…
- Dissimilar objects (e.g. wood and metal) can feel warmer or colder even though both are at room temperature!
Temperature is really a comparative measurement to tell if an object is hotter or colder than something else.

2. Thermal Equilibrium Thermometer
When two objects are in contact with each other for a long period of time, we say they are in thermal equilibrium.
i.e. they both have the same temperature.
This is the basis for temperature (comparative) measurements.
Thermometer
Invented by Galileo to indicate “degrees of hotness”.
As captured air in bulb is heated or cooled it expanded or contracted and liquid level changed accordingly.
Thermometers tell us whether something is hotter or colder on an internationally recognized reference scale.
scale
Thermoscope
captured air in bulb
liquid:
water /wine?
Thermometer use: - fluid (liquid, gas) expansion
- electrical resistance change;
- changes in color…

3. Fahrenheit scale (G. Fahrenheit, 18th century)
Temperature Scales
Thermometers are based on reliable reference points such as freezing and boiling point of water. (Stable points as phase transition).
Want the reference points to be far apart – with a uniform scale in between.
Fahrenheit scale (G. Fahrenheit, 18th century)
He did not want to deal with negative values. So he set his “0” mark at the coldest temperature he could make in the laboratory (using mixture ice, water and salt).
He set his upper reference to human body temperature and called it 96 º (for easy division by half, quarter etc.).
This resulted in scale (still in use in U.S.A.) where freezing point of water = 32 ºF and boiling point = 212 ºF (at sea level).
There are 180 ºF between these two common reference points.

4. Celsius scale (A. Celsius, 18th century)
He used freezing and boiling point of water for reference points and then divided the distance between them by 100 equal parts.
Strangely, he set the temperature of freezing water to 100 º and boiling water to 0 º!
Later revision resulted in the Celsius (or centigrade) scale with 100 degrees between reference points.
Each Fahrenheit degree is therefore smaller than a Celsius degree:
180 ºF = 100 ºC or 9 ºF = 5 ºC or
Example: What is room temperature of 68 ºF in ºC?
This is 36 ºF above freezing point of water (32 ºF).
36 ºF = x 36 ºC C 5 F 1 = 9 5 C 9 F
As 1 = 5
= 20 ºC 9
Thus: 68 ºF = 20 ºC

5. Conversion Between ºF and ºC
Tf = Tc + 32 9 5
Tc = (Tf – 32) 5 9
=>
i.e. multiplying Tc by tells us how many degrees Fahrenheit above freezing.
Example: At what temperature do the Celsius and Fahrenheit scales have the same value?
set Tf = Tc to determine value…
or Tf = Tc = -40 º (F or C) 9 5
-40 32 20 68
100
212 ºC ºF
Tf = Tc + 32 9 5
Tf = Tf + 32 9 5
So when the temperature gets close to -40 º it does not matter which scale to use!
At higher and lower values they are quite different!

6. Absolute Zero Temperature
Choosing the freezing point of water to be 0 ºC is a convenient but arbitrary decision.
Negative temperatures (ºC and ºF) are common in mountainous regions…
pressure
temperature (ºC)
-300
-200
-100
200
100
different gases
liquid /solid
The idea of an absolute zero temperature arose from observations of changes in gas pressure with temperature.
As gas cools it reduces
in pressure until it
liquefies /solidifies.
Gas pressure decreases linearly with temperature.
Extension of these cooling lines for different gases all intersected at one temperature at zero pressure: ºC.
As negative pressure has no physical meaning, this indicates that temperature cannot fall below ºC.

7. Kelvin Scales (after Lord Kelvin 19th century)
The Kelvin (or absolute) scale has “0” at ºC
Uses the same degree intervals as Celsius scale.
To convert Celsius to Kelvin simply add
T = Tc
As Kelvin is an absolute scale, the comparative “degree” symbol is not used.
Example 1: What is room temperature of 20 ºC in K?
T = Tc
Example 2: Nitrogen (N2) gas liquefies at 77 K. What is its temperature in ºC and ºF?
Tc = T =
= K (or 293 K) =
= ºC
Tf = Tc + 32 9 5
= ( ) + 32 9 5
= ºF

8. Temperature Ranges Incredible range of temperatures in universe! 0 K
Absolute zero ºC
4.25
Liquid He boils
-268.9
20.4
Liquid H boils
-253 77
Liquid N2 boils
-196 90
Liquid O2 boils
-183
194
CO2 (dry ice) freezes
-79
273
Water freezes
310
Body temperature
~ 37
1336
Gold melts
1063
5773
Carbon arc
5500
6273
Sun’s photosphere
6000
6293
Iron Welding arc
6020
Incredible range of temperatures in universe!

9. Types of Thermometers
Mercury thermometer: expansion of Hg in narrow tube (used for everyday temperature ranges).
Thermocouple: uses two different metals to generate a voltage between hot and cold junctions (range:-270 to 2300ºC)
Platinum resistance: electrical resistance increases with temperature (range: -270 to 700 ºC)
Thermal imaging (thermograph): all objects emit infra-red radiation. As temperature increases the infra-red intensity increases (used for a broad variety of applications).

10. Thermal Imaging (Thermogram)
Carcionoma (elevated temperature)
Abnormally high temperatures in the Pacific Ocean associated with El Nino ( )
Vascoconstriction (decreased temperature 34-28ºC)

11. Thermal Expansion
An ancient knowledge – we all know that substances (solids, liquids, gases) expand when heated (and vice versa).
Linear expansion: (rod, bar etc)
The change in length of a solid bar (ΔL) depends on:
- change in temperature ΔT
- original length L0
- Coefficient of linear expansion, α
ΔL = α. L0. ΔT (where: ΔT in K or ºC)
Expansion occurs at the atomic level. As heat bar atoms vibrate with larger amplitude and their mean separations increase … This causes an expansion of the whole rod.
Objects continue to expand until they melt (change state).
ΔL expansion is a percentage variation - depends on original length L0 .
Example: 5% of 1m = 0.05 m, but 5% of 10 m = 0.5 m

12. Coefficients of Thermal Expansion for Solids and Liquids (ºC)-1
Note:
(β = 3α)

13. Thermal Expansion

14. (For a shorter bridge the length and height change would be less.)
Example: An opening steel bridge of length 250 m has no gap at 18ºC. Determine the height of the bridge when the temperature raises, 20ºC.
α = 12 x 10-6 (ºC)-1 h
125m
ΔL = α. L0. ΔT
ΔL = [12 x 10-6 (ºC)-1] (125m)(20ºC)
= .03 m (ie.3 cm)
h = [(125.03m)2-(125m)2]½
h = 2.74 m
(For a shorter bridge the length and height change would be less.)

15. Volumetric expansion (Solids and liquids):
Expansion of Holes
What happens to the size of a hole when a material with a hole in it expands?
When the individual tiles expand, the hole also expands!
The expanded hole is the same size as the heated tile.
Result: A hole (of any shape) in a solid material, therefore expands or contracts just as if it were made of the material that surrounds it.
Volumetric expansion (Solids and liquids):
Analogous to linear expansion, volumetric expansion:
ΔV = β.V0.ΔT (Note: β ≈ 3 times α for solids).

16. Temperature Extremes
Highest temperature likely to exist occur at center of certain stars, T ~ 4 x 109 K (a theoretical extreme).
At ~1010 K matter will fragment into subatomic particles!
A hydrogen bomb ignites at ~ 4 x 107 K and blazes to 108 K!
Center of Sun only 1.5 x 107 K (15 million K)
Atoms (matter) is formed within stars at >105 K.
Liquid helium (4.25 K) is most exotic of all cryogenic materials.
Liquid He can be cooled (by pumping) to 2.18 K where it undergoes a dramatic change – not a solid but a superfluid with wonderful properties: superconductivity.
Lowest temperature achieved ~2x10-8 K!
At such temperatures atoms almost stationary? But He still a liquid (zero point energy).

18. Bimetallic Strip
Made of two strips of metal joined together but having different coefficients of linear expansion.
Often brass (α = 19x10-6 ºC -1) and steel (α = 12x10-6 ºC -1) are used.
When heated (cooled) the brass expands (contracts) more than the steel and the strip bends.
Bimetallic strips frequently used in electrical switches to automatically adjust temperature.

19. Expansion is usually quite small – typical metals expand about 7% when temperature rises from near 0 K to its melting point.
Most materials have a positive coefficient of linear expansion (except rubber under tension shrinks!)
Coefficient α depends on atomic structure. E.g. lead is a soft metal that is easily melted and its atoms are less tightly bound. It therefore has a high coefficient of expansion (29x10-6 K-1).
In comparison, Pyrex glass has very low value of α (3x10-6 K-1) and quartz even lower (about 50 x less than lead).
Result: Buckled railroad track if rails too long.
Now we use very low expansion steel alloy to stop buckling of continuous track.
Volumetric expansion (Solids and liquids):
Analogous to linear expansion, volumetric expansion:
ΔV = β.V0.ΔT (Note: β ≈ 3 times α for solids).

22. Liquids are not bound like solids and their volume coefficient of expansion is much larger (around 50 times) that of a solid volume.
(Note: Both α and β are dependent on temperature as well.)
Results:
Bimetal strip bends when heated – used for thermal sensor switches, car indicators…
Bridges expand in summer (and vice versa) – need expansion joints. E.g. Bay bridge in San Francisco contracted 1.3 m in 1937!
Dental fillings have same coefficient of expansion as teeth to stop them cracking!
Loosening metal lids on glass jars – metal expands more than glass when warmed.

24. Temperature and Heat
Temperature of a body is a measure of the average kinetic energy of its constituent atoms.
Temperature of a substance is not dependent on the type and number of atoms present (i.e. mass).
In contrast:
Heat (thermal energy) of a body is a measure of the total net K.E. possessed by the constituent atoms /molecules in motion.
The thermal energy depends on the total number of atoms present and on their average K.E. (i.e. temperature).
Example 1: The thermal energy (heat) stored in the Atlantic Ocean is enormous but the average K.E. of its molecules is low and hence its temperature is low.
Example 2: In nuclear reactions the temperature of a gas can be millions of degrees but its mass is very low and hence its heat content is low.