Heat Energy  
Sources of Heat Energy
Chemical Potential Energy - Energy that is bound up in chemicals.  This energy is usually thought of as the kinetic molecular energy of the moecules and the energy associated in the bonds.
 
Electrical Potential Energy - Energy that is associated with the movement of electricity, usually through a resistor that produces a release of heat because of resistance.
 
Nuclear Potential Energy - Energy associated with the strong and weak forces in a nucleus.  Fission and fusion reactions create atoms that have less energy than  the atoms from which they were made.  This loss of energy is usually released in differnet forms, heat being only one of them.
 
Mechanical Energy - Energy that is released due to friction and compression.
 
Geothermal Energy - Energy associated with the Earth.  Usually caused by the Earth's fluidic magma coming in contact with ground water.
 
Thermometers and Liquids:
Thermometer - from the Latin Thermos or heat.  A device used to measure the kinetic energy (thermos) of something else.  Thermometers work because at a microscopic level liquids expand when they gain energy.  As a liquid gains energy the molecules of the liquid move faster.  Since the molecules move faster they collide more often.  More collisions mean that the molecules push their neighbours further apart.  At a macroscopic level we see the liquid expand up the bore of the thermomter tube.
 
The corollary of this is the cooling of a liquid.  Cooling is  aloss of heat energy.  A loss of heat means a loss of kinetic energy and a slowing down of the molecules.  A slowing of the molecules means fewer collisions and the molecules take up less space.  They can pack in closer together and we see the liquids contract or shrink when cooled.
 
Thermometers cannot measure extreme temperatures because they reach the point where they solidify when cooled or boil when heated.  Temperature by definition is a measure of the average kinetic energy available in an environment. i.e. At 0 K there is 0 J of energy and 0 kinetic energy.  At 0 K all motion has stopped, even the vibrational movement of molecules.  As we increase the temperature substances first begin to vibrate, then melt into lquids, then expand, then boil, then expand again as gases.
 
Ancient Theories of Heat
Four Element Theory - All matter is made up of combinatiosn of Earth, Air, Fire and Water.  ie. Add fire, matter warms up.  Cooling is the removal of fire from the matter.
 
Caloric Theory - An attempt at quantifying the fire. There were thought to be particles called "calorics".  An object gained "calorics" as it warmed and lost "calorics" as it cooled.  These "calorics" came from fire as the matter was warmed.  i.e. fire was a source of calorics and calorics where transferred from a hot substance to a cooler substance or lost to the environment as something cooled.  Count Rumford of Bavaria disproved this theory.  If there was such a thing as a caloric then the particle must has a mass.  Therefore when something warms up there must be an increase in mass.  When something cooled there must be a decrease in mass.  Using very careful measurements on brass cannons that were being bored, Count Rumford noted that a tremendous amount of heat was being liberated due to the boring but no change in mass was observed.  i.e. the mass of the block of brass was equal to the mass of the cannon and the brass turnings.  If the caloric theory was true then the cannon and turnings should have weighted much less because the cannons got very hot during boring and this heat was observed to be lost to the air around the boring machine.
 
Modern Theory of Heat The Kinetic Molecular Theory (KMT)
1.  All matter is composed of atoms and/or molecules which are referred to as particles.
2. The particles of matter are in constant motion.  this motion can be vibrational, rotational or translational in nature.
3. The motion of a particle increases as the temperature increases.  Particles at higher temperatures move faster.  Particles at lower temperatures move slower.
4.  Particles are attracted to one another.  this attraction is due to electrostatic forces. (ionic, dipole-dipole, hydrogen bonds or Van Der Waals forces.  Forces in a solid are stronger than those in a liquid.

 
Heat Transfer
The KMT theory can be used to explain the process of heat conduction. When one end of a rod of metal is warmed the particles a tthat end gain energy and vibrate more rapidly.  They collide with the cooler particles next to them.  the cooler particles in turn speed up due to the collision.  They in turn collide with their neighbours.  This action continues in a chain reaction along the metal.
 
Solids conduct heat, liquids and gases display heat convection. Heat also can be radiated.  Heat is actually part of the electromagnetic spectrum.  Remember that infrared heat from the electromagnetic spectrum chart.  It radiates just like any other form of  light radiation.
 
Since heat is a form of radiant energy it can be transmitted (passed through an object), it can be absorbed (taken into an object and stored) or it can be reflected (bounced off an object).
 
Measuring Heat
Definitions:
Joule (J) - named after James Joule. Labelled in an equation as "q", a unit of energy.   It requires 4.184 J to raise the temperature of 1 gram of water by 1 oC.
 
Watt (W) - after James Watt.  A derived unit:   1 Watt  = 1 J/second
 
Sample Problem #1    An electric kettle delivers 144,00 J of energy to the water in it in 2 minutes.
What is the power of the kettle?

P = Q/t =  144,000 J / 2 min * 60 sec/ min = 144,000 J / 120 sec = 1200 J/s = 1200 W
 

Sample Problem #2     A 100 watt immersion heater used in a tropical fish tank is used to heat the water in a beaker for 3 minutes.  How much energy was transferred to the water?

P = Q/t  therefore   Q = P * t = 100 W * 3 min = 100 W * 180 sec = 18,000 J = 18 kJ
 

The Capacity to Hold Heat
When heat is added to a substance it's temperature increases.  There is a direct relationship between the temperature reached and the heat added.
 
There is another direct relationship between the mass of a substance and the heta needed to make the substance undergo a given change in temperature.
 
Water is the principle substance used because it was water that was used to define the energy unit and water is readily accessible and relatively safe to use.
 
Imperial Heat Unit
The calorie (cal) was defined to be the amount of heat required to raise 1 gram of water by 1 degree Celsius.
If you had 100 grams of water it would take 100 calories of heat energy to raise it's temperature by 1oC.
 
This is became a definition and was called the Specific Heat Capacity. The symbol used in equations to describe the Specific Heat Capcaity is 'c' and the units are J/goC
 
For example the Specific Heat Capacity of water is 1 cal/goC = 4.184 J/goC (Metric definition)
 
Heat Capacity is either the amount of heat required to increase the temperature of a substance by 1.0 oC or the amount of heat released to the environment to cool a substance by 1.0 oC
 
Specific Heat Capacity Table
Substance Specific Heat Capacity 
at 25oC in J/goC
H2 gas 14.267
He gas 5.300
H2O(l) 4.184
lithium
3.56
ethyl alcohol
2.460
ethylene glycol
2.200
ice @ 0oC
2.010
steam @ 100oC
2.010
vegetable oil
2.000
sodium
1.23
air
1.020
magnesium
1.020
aluminum
0.900
Concrete
0.880
glass
0.840
potassium
0.75
sulphur
0.73
calcium
0.650
iron
0.444
nickel
0.440
zinc
0.39
copper
0.385
brass
0.380
sand
0.290
silver
0.240
tin
0.21
lead
0.160
mercury
0.14
gold 0.129
To calculate the Specific Heat Capacity you need the following equation:   Q = mc ΔT
 
c = Q / m ΔT       where  c is the specific heat capacity
                                              Q is the energy
                                              m is the mass of the substance
                                            ΔT is the temperature change
 
Sample Problem #3
An immersion heater isused to warm 500 grams of a liquid from 35oC to 55oC.   If 20 kJ of neergy are given to the liquid, determine the specific heat capacity and use it to suggest an identity for the liquid.
 
c = Q/m ΔT = 20 kJ / 500 g * (55oC - 35oC) = 20,000 J / 500 g * 20oC =  2.00 J/goC
 
Based on the calculated value of 'c' the substance may be vegetable oil.
 
Principle of Heat Transfer
This comes from an understanding of the Law of Conservation of Mass and Energy.  You know that hotter objects transfer heat energy to colder objects.  Hotter objects get colder, colder objects get hotter.
 
             QHeat Released by the Hot Object = QHeat Gained by the Cold Object

              since Q = mc ΔT

              then       mhch ΔTh  =   mccc ΔTc
 

and if both substances are the same then ch = cc can be elimnated.  (where ch is the specific heat capacity of   the hot substance and cc is the specific heat capacity of the cold object.)
 
mh ΔTh  =   mc ΔTc

 
Sample Problem #4
If 80 grams of water at 70oC is mixed with a caertain mass of cool water at 20oC, the final temperature of the mixture is 60oC.  What is the mass of the cool water.
 
Qh = Qc
mhch ΔTh = mccc ΔTc
since we are using water for both the hot and cold sides of the equation we can cancel out the ch = cc
therefore
mh ΔTh = mcΔTc
 
mcmh ΔTh   = 80 g X (Ti  -  Tf)    =  80 grams X (70oC - 60oC)   = 80 g X 10oC   =  20 grams
            Δ Tc             (T- Ti)                       (60oC - 20oC)                         40oC
 
The initial mass of the cold water used was 20 grams.
 
Sample Problem #5
If 400 grams of water at 60oC are mixed with 100 grams of water at 10oC, what is the final temperature of the mixture?
 
            Qh = Qc
            mh ΔTh = mcΔTc
            400 g X (60oC - Tf)  =  100 g X (Tf - 10oC)
            24000 - 400Tf oC = 100Tf oC - 1000
            25000 = 500Tf oC
            Tf  = 25000/500 oC = 50oC
 
Sample Problem #6
A piece of metal with a mass of 500 grams and unknonwn specific heat capacity is placed in boiling water at 100oC.  The hot metal is then transferred quickly into a 200 grams sample of water at 20oC.  If the final temperature of the water-metal mixture is 30oC what is the specific heat capacity of the metal and identify the possible identity of the metal.
 
            Qh = Qc
            mhch ΔTh = mccc ΔTc

            ch = mccc ΔTc   =  200 g X 4.184 J/goC X 10oC   =  0.239 J/goC
                      mh ΔTh               500 g X 70oC

            The metal is probably silver.

            Go to the Specific Heat Worksheet