1. Temperature & Heat
AP Physics

2. Temperature ~American Heritage Dictionary 3 Scales
A measure of the average kinetic energy of the particles in a sample of matter, expressed in terms of units or degrees designated on a standard scale
~American Heritage Dictionary
3 Scales
Scale
Boiling Point of H2O
Freezing Point of H2O
Absolute Zero
Fahrenheit
Celsius
Kelvin

3. Zeroth Law of Thermodynamics
Thermal Equilibrium
Two systems are in thermal equilibrium if and only if they have the same temperature. Two systems that are each in thermal equilibrium with a third system are in thermal equilibrium with each other.
Zeroth Law of Thermodynamics

4. Thermal Expansion
Most materials expand when their temperature increases.
Linear Expansion
Expansion in one dimension (usually the length)
change in length is proportional to the change in temperature
Material
α (1/oC)
Aluminum
24 x 10-6
Brass & Bronze
19 x 10-6
Copper
17 x 10-6
Steel
11 x 10-6
Concrete
12 x 10-6

5. Expansion of Railroad Tracks
A steel railroad track has a length of m when the temperature is 0oC. What is its length on a hot day when the temperature is 40oC? α = 11 x 10-6 (oC)-1

6. James Joule and Heat
James Joule discovered by various means that he could heat a body of water by purely mechanical means:
by lowering a weight and letting a paddle wheel stir the water
by passing electric current through a resistor
by compressing a piston immersed in the water
by friction from rubbing blocks together.
He found that about 800 foot-pounds ( 1 kilo joule) of work could raise the temperature of one pound (.45 kilograms) of water one Fahrenheit degree (0.55oC).

7. Heat flow is energy transfer.
Heat (Q)
Energy that is transferred from one object or system to another object or system as a result of a temperature difference.
(The concept of heat only has meaning as energy in transit.)
Heat flow is energy transfer.
Units: Joule (J), calorie (cal), Calorie (Cal), British thermal unit (Btu)
Unit Relations
Joules
calories
Calories
Btu 1
0.239
2.39 x 10-4
9.48 x 10-4
4.186
0.001
3.97 x 10-3
4186
1000
3.97
1055
252
0.252
The calorie is defined as the amount of heat required to raise the temperature of 1 gram of water from 14.5oC to 15.5oC.
One Btu is defined as the quantity of heat required to raise the temperature of 1 pound of water from 63oF to 64oF.

8. Specific Heat Capacity
Quantity of heat needed to change the temperature of a system is dependent on three things:
The quantity of the temperature change.
The mass of the system.
The nature of the material.
The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the mass m of substance being heated;

9. Down with the Sickness
During a bout with the flu, an 80 kg man ran a fever of 2.0 Co. His body temperature was 39.0oC (102.2oF) instead of the normal 37oC. Assuming that the human body is mostly water, how much heat was required to raise his temperature by that amount?
Material
c [J/(kg·K)]
Water
4.19 x 103
Ice (-25oC to 0oC)
2.01 x 103
Aluminum
0.91 x 103
Salt
0.88 x 103
Iron
0.47 x 103
Silver
0.23 x 103

10. Circuitry Overload
You are an electric engineer designing an electronic circuit element made of 23 mg of silicon. The electric current through it adds energy at the rate of 7.4 mW (7.4 x 10-3 J/s). If your design doesn’t allow for any heat transfer out of the element, at what rate does its temperature increase? The specific heat capacity of silicon is 705 J/(kg·K).

11. Cooling a hot ingot
Ingot - metal that is cast in the shape of a block for convenient handling A kg ingot of metal is heated to 200.0oC and then dropped into a beaker containing kg of water that is initially at 20.0oC. If the final equilibrium temperature of the mixed system is 22.4oC, find the specific heat of the metal.

12. Phases of Matter Three familiar phases of matter include: Gases
Liquids
Solids
…but there are more than those three including…
plasmas, superfluids, supersolids, Bose-Einstein condensates, fermionic condensates, liquid crystals, strange matter and quark-gluon plasmas

13. Phase Changes What goes on during a phase change?
Transition from one phase of matter to another
What goes on during a phase change?
At a given pressure, phase changes:
usually occur at a definite temperature*
heat is absorbed or released
there is a change in volume of the matter
there is a change in density of the matter
*At this temperature and pressure both phases of matter can coexist, this is called phase equilibrium.

14. Heat Required per unit mass
Types of Phase Changes
Phase Change
Process
Example
Heat Required per unit mass
Solid
 Liquid
Metal gallium melts in your hand
Latent Heat of Fusion (Lf)
Liquid
 Solid
Water freezes
 Gas
Liquid Nitrogen boils at room temp.
Latent Heat of Vaporization (Lv)
Gas
Water vapor condenses
Dry Ice (CO2) sublimes to its gaseous phase at room temp
Latent Heat of Sublimation (Ls)
Frost forms on cold objects
To melt a mass m of material that has a heat of fusion Lf requires a heat Q given by:
To freeze a mass m of material that has a heat of fusion Lf requires a heat Q given by:

15. A Closer look at Phase Changes
To cause a phase change energy must be absorbed or released by the object/system. During the phase change the heat energy does not change the temperature of the object.

16. DO The Dew
A physics student wants to cool 0.25 kg of Mountain Dew (mostly water and high fructose corn syrup) initially at 20oC by adding ice initially at -20oC. How much ice should she add so that the final temperature will be 0oC with all the ice melted? Assume that the heat capacity of the container may be neglected.

17. Heat Transfer There are three mechanisms of heat transfer. Radiation
Convection
Conduction

18. Radiation
Energy transfer through electromagnetic radiation (fancy words for light)
Ex.

19. Convection Energy transfer of heat by the motion of a mass of fluid
Ex.

20. Conduction
heat transfer through a material from regions of higher temperatures to regions of lower temperatures
Good thermal conductors are metals because they have many free electrons
Ex.
Rate of Heat Transfer…Heat Current (H)

21. Rate of Heat Transfer (H)
The rate of heat transfer through a material with regions of varying temperatures is:
proportional to the cross sectional area A.
proportional to the temperature difference ΔT.
inversely proportional to the distance between the regions L.
The constant of proportionality is the thermal conductivity of the material k.

22. Cooler Conduction
The StyrofoamTM box seen below is used to keep drinks cold at a picnic (or wild beach party whatever suits your taste). The total area of the sides, top, and bottom is 0.80 m2, and the wall thickness is 2.0 cm. The box is filled with ice and Root Beer, keeping the inner surface at 0oC. What is the rate of heat flow into the box if the temperature of the outside surface is 30oC? How much ice melts in one day (24 hr.)?
Material
k (W/(m·K)
Silver
406
Copper
385
StyrofoamTM
0.01
Wood
0.12 – 0.04
Air
0.024

23. Conduction In Series
A steel bar 10.0 cm long is welded end to end to a copper bar cm long. Each bar has a square cross section, 2.00 cm on a side. The free end of the steel bar is in contact with steam at 100oC, and the free end of the copper bar is in contact with ice at 0oC. Find the temperature at the junction of the two bars and the total rate of heat flow.
Material
k (W/(m·K)
Steel
50.2
Copper
385