Thermodynamics� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �� � � � � � � � � � � � � �
•� � � � ! " # $ % & ' ( ! ) * " + , ' ( ! ) * " + * - . ! / # ! % " * - 0! " ! % 1 + ! , 2 3 , & , # ! ( , 4 1 2 5 ! % " ! 6 7 & 8 ! 9 # 2 " : , - * 9 , ;( 2 # +5 * # ! 6 7 & ( 2 # +2 " 2 3 ! - ! , # + * - 2 7 < ! # , . = - * " ! # ,* % 2 $ " 6 # ) ! , $ " 0•� > � � * " 6 � ? � � ! " # $ % + ! , ' # ) ! % ( 2 6 & " * ( + , ' + " # ! % " * -! " ! % 1 & 2 3 , & , # ! ( , * " 6 +# , % ! - * # + 2 " # 2 9 2 % @ ; A " 6 $ , # % + * -% ! 5 2 - $ # + 2 " B C - ! # % + +# & * " 6 ( * 1 " ! # + , ( ' 2 " ! = # , 2 3 ) * % 1 ! 4 3 + ! - 6 4 % * 6 + * # + 2 " B•D E � � ! " # $ % & ' % ! - * # +5 +# & * " 6 F $ * " # $ ( ( ! ) * " + , ; # ) !- * 9 , 2 3 # ) ! * # 2 ( + 9 2 % - 6
Some History
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� � � � � � � � � � � � � � � � � � � � � � � � � �•
� � � � � � � � � � � � � � � � �•
� � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � �•
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� # # ) + , = 2 + " # 4 * - - # ) + , , 2 $ " 6 , = % ! # # & * 7 , # % * # 4 # ) 2 $ 1 ) �
We know what work is, but…What is heat?
• Work: mechanical energy• Heat: thermal energy…� � � � � � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
But what is energy?But what is energy?But what is energy?But what is energy?“We have no knowledge of what energy is …it is an abstract thing…” (Richard Feynman)
Definition 1: a scalar quantity that describes the amount of work that can be performed by a force
Definition 2: Energy is a property or characteristic (or trait or aspect?) of matter that makes things happen, or, in the case of stored or potential energy, has the "potential" to make things happen.
By "happen", we mean to make things move or change condition. Examples of changes in condition are changes in shape, volume, and chemical composition (results of a chemical reaction). There are also changes in pressure, temperature, and density which we call a "change of state" in thermodynamics. Phase changes, such as changing from solid to liquid, or liquid to vapor, or back the other way, are also good examples of condition changes. Something happened!
Good, but what about radiation?
My definition of energyMy definition of energyMy definition of energyMy definition of energyDefinition 3: a scalar quantity conveniently defined so that it is conserved
in all physical processes taking place in a closed system, and that obeys certain symmetry principles.
Energy comes in many inter convertible forms:
-internal (atomic motion in solids, liquids & gases)-electrical & magnetic-chemical - in molecular bonds (coal power)-kinetic (wind power)-potential – gravitational (hydropower)-radiant (solar power)-nuclear – in proton-neutron bonds (nuclear power)…
ENERGY obeys conservation laws!!!
What is work?Mechanical work: scalar quantity describing the amount of energy transferred by a force acting through a distance
dFW .=Units: [W] = [F].[d] = N.m (Newton.meter) = J = Joule
Kinetic-Molecular Theory�� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � ��� � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � �� � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � ! " # $ � � � � � � � � � � � � � �� � � � � �� � � � �% � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � & � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � �
Internal energy' � � � � � � � � � � � � � � � � � � � � � � � � � � � � (� � � � � � � � � � � � � � ) � � �� � � � � � � � � � � �� � � � � � � � � � �� � � � � � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � % � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � * � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
Internal Energy (contd.)� � � � � � � � � � � � � � ( � �� � � � � � � � � � � � � � � � � � � � ) � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � % � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � �� � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � % � � � � � � � � � % � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � ( � � � � � � � � � � � � � � � � � � � � � �� � % � � � � � � � � � � � � � � � � � � � � � � � % � � � � � � )� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � �� � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � �� � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � �� � � �� � � � �� � � � � � � � � � � � � � � � �http://mutuslab.cs.uwindsor.ca/schurko/animations/particlesinmetals/eqilibrium-v1.htm
Temperature vs. Internal Energy� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � ��� � � � � �� � � � � �� � � � � � � � � � � � � � � �� � � �� � � � � � �� � � � � � � � � � � � � � � � � � ! " � # ! ��� � � � $ � � % & % � ' �( � � � �� � � � � � � � � � ) � � � � � � � � � � � � � � � � � � � ) � � � � ) � � �� � � � � � � � � � � � � � � ��� � � �� � � � � � � � � � � $ � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � * � � �� ��� � � � � � � $ � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � ) � � � � � � � �� � � �� � � � � � � � � � � �� � � � � � � � � � � � � � � � ) � � � � �$ � � � � � � � � � � � � � � � � ) � � � � � � � �� � � �� � � � � � � � �$ � � � � � � � � � � � � � � � �� � � � � � � �+ , � � � � �� � � � � � � �� - . � � � � � ) / 0 0 0 � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��� � � � � � � � � � � � 1 � � ) � � � � � � � $ � � � � � � �� � � � � � � � 1 1 � � � � � � � � � � � � � � � � 1 � � 2 � � ) � � � � � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � $ � � � � � � � � � � �� � � � � �� � � � � � �http://www.absorblearning.com/media/item.action?quick=ad
Internal Energy vs. Heat� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��� � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � % � � � � � � � � � � � � � � � �� � � � �� � ( � � � � � � � � � � � � � ) � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � �
Summary of concepts•
� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �• � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � �� � � �� � � � � � � � � � � � � � � � �• � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � �
http://mutuslab.cs.uwindsor.ca/schurko/animations/particlesinmetals/eqilibrium-v1.htm
CPS question: Which one is “colder”(has lower temperature?)
ICEBERG
ICE CUBE
a) The iceberg
b) The ice cube
c) They both have the same temperature
CPS question: Which one has more “internal energy”
ICEBERG
ICE CUBE
a) The iceberg
b) The ice cube
c) They both have the same energy
What is Heat? What causes it?� � � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �
The Concept of Temperature•Without realizing its significance, Galileo (ca 1630) developed a crude thermometer
•Fahrenheit (1715); measured temperature by expansion of a fluid (mercury)•Celsius (1742) defined 0oC as the melting point of ice; 100oC as the boiling point of water; with a scale in between linear with expansion of fluid•Lavoisier (1780) realized that matter is composed of discrete atoms and molecules •Dalton (1808), temperature interpreted as a measure of particle speed (gas) or vibration (solid) •Kelvin (ca 1885) introduced the notion of the absolute zero temperature,where all atomic motion stops
Measuring temperature (cont)–
� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � �� � � � % � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �–
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � % � � � � � � � � � � � �–
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � ' � � � � � � � � � � � � � � �� � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �
The illustration shows a thermometer that uses a column of liquid (usually mercury or ethanol) to measure air temperature. In thermal equilibrium, this thermometer measures the temperature of
A. the column of liquid.
B. the glass that encloses the liquid.
C. the air outside the thermometer.
D. both A. and B.
E. all of A., B., and C.
CPS question
Temperature scalesValues on the temperatures scales (Fahrenheit, Centigrade/Celsius, and Kelvin) may be readily interconverted. Physics professors will want values to eventually be in Kelvins because that’s the form in SI units.
Temperature conversionsfrom Fahrenheit � � � � � � � � � � � � � � � � �°( � � � �
°� �
− � � � × � ⁄ � �°� � � �
°( �
× � ⁄� � � �� �� � � � � � � �°� � � � � � ! " � × � # � �
°� � � � � �
× � ⁄� − � � � ! "� � � � � � � � � � $ % % ! " � ' & � � � � � � � � � � � �) �� � � � � � � � � $/°� � � ⁄� °
( � � ⁄� �You only need to remember:
1K = 1 °C
Absolute Zero & the Kelvin Scale� � � � � �� � � � � � �� �� � � � � � � � � � 1 � � � � � � �� � � � � �� � � � � � � � �� � � � � � � � � � � � � � � � �1 � � � $ � � � �� � � � � � � � � � � � � � � � � �� � � � � 1 � � � � � � � � � � � � � � � � � � � �� �� � � " � � / � °( $ � � �� � � ! °
� � . � � � � � � 1 � � � � � � � � � � � � � � � � � � � � $ � � � � � � �� � � � � � � � � � � �� � � � � � � � � � � � � � � �� � �� � � � � � � � � �� � � � � � � � � � � � � � � � � / 0 � � � � �� � � � � ) � � � � � � � 1 � � � � � � � � � � �� � � � � � � � � �� � � � � � � � 1 � � � �� $ �) � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��� � � � � � � � � � � � � � � � � � � � � � � � � � � � � ) � � � � � � �� � � ) � � � � � � � � � � � � � �� � � � �
Thermal Equilibrium� � � � � � �� � � � � � � �� � � � � � � � � � � � � � � � � � � � �) � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � �� � � � � � � � � � � � � � ) � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � �� ) � � � � � � � � � � � � � � � � $ � � � � � � � � � � � � � � � �) ) � � � � � � $ � � � � � � � � � � � � � � �� � � � � � � � � � $ � � � � � � � � � �� ) � � � � � � ) � � � � � � � � � � � � � � � �� � �� � � & % & ' �heat� °� �
°�� & % ! % ! � % � ' & �� � � � � � � �� � � � � � � � � � � � � � � � � � � � $ � � � � ) � � � � � � � � � � � � � � � � � � � � � � � �� � � � � �� � � � � ) � � � � ) � � � � � � � � � � � � � �
http://jersey.uoregon.edu/vlab/Thermodynamics/index.html
The 0th law of thermodynamics� � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � �� � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � ��� � � � � � �� � � � �� � � � � � � � � � � � � � � � � � � � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � �� � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
�
Effects of heat:
•expansion of a body•producing mechanical work•increasing the temperature of a body•melting a body•vaporizing a liquid•Liquefying a gas
Phase transitions
Thermal expansion—linear• A change in length will
accompany a change in temperature. The size of the change will depend on the material.
• The change in length is proportional to the temperature change and the initial length:
TLL ∆=∆ 0αα is the linear expansion coefficient and is material dependent
Nice property for building thermometers! (e.g. mercury)
A. illustration #1
B. illustration #2
C. The answer depends on the material of which the object is made.
D. The answer depends on how much the temperature increases.
E. Both C. and D. are correct.
CPS question
A solid object has a hole in it. Which of these illustrations more correctly shows how the size of the object and the hole change as the temperature increases?
#1
#2
http://freedrive.com/file/831762
Measuring Heat– � � � �� � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � �� � �� � � � � � � � �� � � � � �� � � � � � � � � � � � �� � � � � � � � � � �–
� � � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � �Quantity of Heat
Calorie: amount of heat needed to raise the temperature of 1 gram of water from 14.5 °C to 15.5 °C
Since heat is another form of energy, there must be a relationship between these units and the familiar mechanical energy units. Experimentally, one finds:
1 cal = 4.186 J
The calorie is NOT a fundamental SI unit. The Joule ISthe standard unit of energy
Specific heat –
� � � � � � � � ) � � � � � � � � � � � � � � �� � � � � � � � � � � � ) � � � � � � ) � � � � � � � � � �� �� � ∆ � � � ) � � � � � � � � �� � � � � � � � � � � �∆ � -
–+ � � � � � � � � � � - . � � � �) � � � � � � � � � � � � ��� � � � � � � � � � � � � � � � � � � � � � � � � � � �� �� � � � � � � � ) � � � � � � � � � � � � � � � � � � �� � �� � � � � ) � � � �
– � � � � � �� � � � � � � � �
– � � � � �� � � � � � � � � � � � � � � � � � � ) � � � �� � � � � � � � � � / � � � � ) � � � � � � �� � � � � � � � � � � � � / � ( -TmcQ ∆=
For water: c = 1 cal/(g C�)=4190 J/(kg K)
http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/thermochem/heat_metal.html
SI units
Definitions:
Heat Capacity of a system is the amount of heat required to change the temperature of the whole system by one degree. It’s an extensive quantity.
Specific Heat is the amount of heat required to change temperature of one kilogram of a substance by one degree.
Heat capacity = Specific Heat x Mass. C=c.m
Avogadro constant
Molar Heat Capacity specific heat in units of “Moles”, a certain number of atoms (Avogadro constant)
Specific heat values
?
LARGE !!!
Small !!!
Small !!!
(Dulong and Petit)
Phases of matterPhases of matter
Water, Steam, Ice
Water exists in a few phasesWater exists in a few phases
•Liquid•Solid (ice)•Gas (steam)
� � �� � � � �� � � �� � � � � � � � � � � �� � � � � � �� � � � � � � � � � � � � � � � �GasGas� � � � � �� � � � � � � � �� � � �� �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � �� �� � � � � � � � � � �
LiquidLiquid� � � �� � � �� � �� � � � �� � � � � � � �� � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � �� �
SolidSolid� � � �� � � �� � � � � � � � � � � � �� � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � �� � � � � � � � � � � � � � �
Generally:Generally:•Liquids denser than gas•Solids denser than liquids
Not water!Not water!
+ � � ) �� � � � � �) � � � � � � �� � � � � � � *Water most dense at 4 CWater most dense at 4 C
Phase equilibriumPhase equilibrium� � � �� � � � � � � � � � � � � � � � � �� � � � � � � � � � � �� � � �� � � �� � � � � � � � � � � � � � � � � � � � � � � � �� � � � �� � � � � � �� � � � � � � � � � °�� � �� � � � � � � � � � � � � �� � � °�
Phase transitionsPhase transitions
•Transformation from one phase to another
•Absorbs/releases latent heat (energy in bonds)
•Represents a change in orderWhenever a substance undergoes a phase transition,
energy is transferred into or out of the substance WITHOUT causing a change in temperature.
Example: Phase transition Example: Phase transition -- meltingmelting
heat
melting
freezing
evaporation
condensation
sublimation
deposition
� � �� � � � � � � � � � � � � � � � � � � � � � � � �� � � �
Latent heat
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � ) ) � � �� � , � � � � �� � - � � � � ) � � � � �1 � �� � �http://www.absorblearning.com/media/item.action?quick=zw
Video demo: http://www.youtube.com/watch?gl=GB&hl=en-GB&v=1PcnCWZP7l0
Phase transitions: ExampleEnergy required to convert 1 g of ice, initially at -30°C to steam at 120 °C.
Specific Heat of: (in J/g K)
Water: 4.19; Steam: 2.01; Ice: 2.06
Latent heat of fusion: 334 J/g
Latent heat of vaporization: 2260 J/g
Phase transitions Phase transitions can be affected by can be affected by pressurepressure
Summary: Phase changes and temperature behavior
• A solid will absorb heat according to its heat capacity, becoming a hotter solid.
• At the melting point, a solid will absorb its heat of fusion and become a liquid. An equilibrium mixture of a substance in both its liquid and solid phases will have a constant temperature.
• A cold liquid will absorb heat according to its heat capacity to become a hotter liquid.
• At the boiling point, a liquid will absorb its heat of vaporization and become a gas. An equilibrium mixture of liquid and gas will have a constant temperature.
• A cold gas can absorb heat according to its heat capacity and become a hotter gas.
A pitcher contains 0.50 kg of liquid water and 0.50 kg of ice at 0°C. You let heat flow into the pitcher until there is 0.75 kg of liquid water and 0.25 kg of ice. During this process,
A. the temperature of the ice-water mixture increases slightly.
B. the temperature of the ice-water mixture decreases slightly.
C. the temperature of the ice-water mixture remains the same.
D. The answer depends on the rate at which heat flows.
CPS Question
Heats of Fusion and Heats of Vaporization
Heat Transfer Processes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � �� � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � ��� � � � � � � �http://www.wisc-online.com/ViewObject.aspx?ID=SCE304
http://www.kangwon.ac.kr/~sericc/sci_lab/physics/conduction/conduction.html
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Radiation and Absortion
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� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �H ! " # $ � � � � � � � � � � � � � � � � � � %� � � � % � � � � � � �
Tenv: Temperature of the environment surrounding the body