Temperature and Heat
Welcome to Thermodynamics
(or welcome to heat transfer)
Up to now: mass, length, time, current
The fourth quantity in physics: Temperature and related another form
of energy, HEAT
What is temperature?
Let’s define it is a variable to measure “hot” and “cold”. (We will see that it
is a measure of an internal kinetic energy)
What is heat?
Energy transferred between objects because of a temperature difference
Transferring an amount of heat to an object may raise its temperature.
Are heat and temperature the same or maybe the change
in Temperature?
NO! Heat neither can be the same thing as temperature
nor the increase in temperature. The amount of heat to
increase temperature depends how much mass and what
material is being heated
Thermal equilibrium
No heat transfer between two objects (when they are in thermal contact)
(Note: a good thermal insulator, doesn’t totally prevent hat transfer, it
just slows it down)
Let’s summarize this in the
Zeroth law of thermodynamics
Two objects are in thermal equilibrium when
their temperature is the same
or
If object A is in thermal equilibrium with B and
B is in thermal equilibrium with C, then A and
C are in thermal equilibrium.
(Is it obvious?)
Let’s begin how we measure temperature……….
Temperature Scales
The Celsius Scale (Anders Celsius 1701-1744)
Reference points:
1. Water freezes at zero degrees Celsius:
0˚C
2. Water boils at hundred degrees Celsius: 100˚C
A change in temperature is described as “Celsius degrees” C˚
Lowest possible temperature -273.15˚C
The Fahrenheit Scale (Gabriel Fahrenheit 1686-1736)
Reference Points:
1. Coldest temperature he was able to achieve in his lab.
2. Body temperature 96 degrees (today 98.6 ˚F). Nobody knows why 96 ˚F
Therefore water freezes at 32˚F and boils at 212˚F
A change in temperature is described as “Fahrenheit degrees” F˚
Be careful!
1 degree is not necessarily not to the same as 1 degree!
Celsius Æ Fahrenheit
9F °
TC + 32°C
TF =
5C °
Fahrenheit Æ Celsius
5C °
TF =
TC − 32°C
9F °
The Kelvin Scale (William Thomson, Lord Kelvin 1824-1907)
Kelvin K = SI Unit
Constant-Volume Gas Thermometer
Pgas = Pat + ρmercuryhg
Extrapolation of linear relationship between pressure and temperature leads to absolute zero (-273.15˚C)
Absolute zero is exactly T = 0K
The difference between Celsius and Kelvin is just a shift of the zero level
T = TC + 273.15
Degrees ˚ is not used in the Kelvin scale !
Thermal expansion (a key issue to build a thermometer)
Most substances expand with temperature (one exception
is water. The fish in the pond are happy about it!)
Thermometer: Fluid in a tube. The height of the fluid is a
measure for the temperature.
Change of length (1 D), area (2 D) and volume (3 D) is
related to temperature: Thermal Expansion
1D – Linear Expansion
ΔL = (const .) ΔT = αL0 ΔT
α : Coefficien t of linear expansion [K ]
-1
2 D Area Expansion
Calculation gives us for area of any shape
ΔA ≈ 2 α A ΔT
3 D Volume Expansion
Calculation gives us for area of any shape
ΔV ≈ 3α V ΔT = β V ΔT
β : Coefficient of Volume Expansion [K -1 ]
If there is no β listed for a certain
substance one use β = 3α
Substance
Coefficient of linear Expansion,
α (K–1)
Substance
Coefficient of volume
expansion, β (K–1)
Lead
29 x 10–6
Ether
1.51 x 10–3
Aluminum
24 x 10–6
Carbon tetrachloride
1.18 x 10–3
Brass
19 x 10–6
Alcohol
1.01 x 10–3
Gasoline
0.95 x 10–3
Olive oil
0.68 x 10–3
Water
0.21 x 10–3
Mercury
0.18 x 10–3
Copper
Iron (Steel)
Concrete
Window glass
17 x
10–6
12 x
10–6
12 x
10–6
11 x
10–6
10–6
Pyrex glass
3.3 x
Quartz
0.50 x 10–6
Special properties of Water (Why the fish are so lucky that the lake
is freezing from the top to the bottom)
Application of thermal expansion: Bimetallic strip
Rub over a piece of wood (or watch the film Castaway how to make fire) and
you can feel that the temperature of the wood increase. Remember that
energy cannot be created or destroyed. But energy can be transferred. For
example, transfer mechanical work into heat.
The first unit of heat was calorie (cal).
1 kcal is defined as the heat to increase the temperature of 1kg water from
14.5°C to 15.5°C.
Connection between heat and mechanical work
James Prescott Joule showed with his machine that
1 kcal = 4187 Joule
or 1 cal = 4.187 J
1000 cal = 1 C (food calorie)
(also called the mechanical equivalent of heat)
Specific Heat
The heat required to increase the temperature of an
arbitrary substance is given by the specific heat, c
Q
c=
[J /(kg⋅ K) = J /(kg⋅ C°)]
mΔT
Öalways positive
ÖIf Q is positive then change in temperature
positive
ÖIf Q is negative then change in temperature
negative
ÖLarge specific heat means take large quantities
of heat with little change in temperature
Example:
Specific heat of 1kg water is cwater = 4186 J/(kg/K)
Calorimetry
(Dropping an object into a lightweight, insulating flask containing water)
QB + QW = 0
mb cb (T − Tb ) + mW cW (T − TW ) = 0
mb cbTb + mW cW TW
T=
mb cb + mW cW
Thermodynamics describes heat transfers. How can we exchange heat?
Three options: Conduction, Convection, Radiation
1.Conduction
Heat flows directly through a material
Heat flow fast Æ good thermal conductor
Heat flow very slow Æ thermal insulator
We find that the amount of heat flowing through an object is ~A, ~ΔT, ~t, ~
1/L
ΔT
Q = kA
t
L
k : thermal conductivity [
W
]
mK
Substance
Silver
Copper
Gold
Aluminum
Steel, low carbon
Lead
Stainless steel—alloy 302
Ice
Concrete
Glass
Water
Asbestos
Wood
Wool
Air
Thermal Conductivity, k
[W/(mK)]
417
395
291
217
66.9
34.3
16.3
1.6
1.3
0.84
0.60
0.25
0.10
0.040
0.0234
Convection
Heat transfer by movement of matter in a fluid.
Forced convection (Fan, Pump)
Natural convection: (Heater,
e.g. circulation - warm air raises up, cold air sink down)
Radiation (there is more or less nothing between earth an sun!)
All objects give off energy in form of radiation and absorb it in same way.
There is no need of transportation of matter – electromagnetic waves
Radiated Power (Energy per time)
Stefan’s Law
P = eσAT
Use Kelvin!
4
Net radiation (s : surrounding T)
Pnet = eσA(T − TS )
4
4
e: emissivity (between 0 and 1)
0 ideal reflector, 1 black body
σ: Stefan-Boltzmann constant = 5.67 10-8 W/(m2K4)