What is heat?
Heat is spontaneous transfer of energy from a hotter body to a
colder one, other than by work or transfer of matter, whenever there is
a suitable physical pathway between them.
KINETIC THEORY OF MATTER
Kinetic Theory of Matter proposes that heat is a measure of
internal kinetic energy of the molecules and atoms making up the
substance
The precise relationship between the average molecular kinetic
energy KEave and absolute temperature T is found to be
KEave = (3/2) kT
(Eqn 11.7)
Where k, known as Boltzmann’s constant, has the value
k = 1.38 x 10-23 J/K
This equation holds for the molecules of all gases of their
molecules.
Using this theory, temperature and heat differ based on the
following definitions;
Temperature – a measure of the average kinetic energy of a system.
Heat – a measure of the total kinetic energy of a system.
INTERNAL ENERGY AND HEAT
How much internal energy a body has depends on its
temperature, its composition, its mass, and its state (solid, liquid, gas).
The temperature of the body alone, however, is what governs whether
internal energy will go from it to another body it is in contact with, vice
versa.
Because heat is a form of energy, the unit of heat is joule.
However, the kilocalorie (kcal) and British thermal unit (Btu) are the
once used specifically for heat energy. To distinguish heat from other
forms of energy, many use the unit kilocalorie.
The kilocalorie is the amount of heat required to raise the temperature of
1 kg of water by 1C.
The relationship between joule and kilocalorie are as follows:
1 J = 2.39 x 10-4 kcal
1kcal = 4185 J
QUANTITY OF HEAT
We said that aside from temperature, heat is also affected by
other factors.
According to the kinetic theory of matter, heat is a measure of
the total kinetic energy of a system, so the amount of matter affects
heat. The amount of matter is just mass.
The movement of the molecules also depends on the type of
material used. Scientists refer to this property as the Specific heat of a
material.
So with these factors in mind, the amount of heat gained or lost
in a system is given by the following equation:
Heat lost or gained = mass x c x Temperature change
Q = mcT
(Eqn. 11.8)
where Q is the heat lost or gained in kcal,
m is the mass in kg,
c is the specific heat kcal/kg C and
T is the temperature change in C.
If you find that you are given c in c/calg C, this equation also
works when heat is in calories, mass in grams, and temperature
change in C.
SPECIFIC HEAT
Specific heat is a property of a material that explains why some
foods and liquids remain hotter longer that others.
The specific heat (c, in cal/kg C) of a material is a number,
which gives us an idea how much heat in calories (or kcal) is needed
to raise the temperature of one gram (or kg, if the heat is in kcal) of the
material by one degree Celsius.
For example,
You are more likely to burn you tongue on the filling of a hot
apple pie than the crust. This tells you experimentally that the apple pie
filling has a greater specific heat that the crust.
capple pie > ccrust
Using our definition, it takes more heat to bring one gram of the
apple pie to a given temperature, and you must also remove more
heat to drop the temperature of the apple pie.
Specific heat of various substances
Substance
Specific heat capacity
(kcal/kg C)
Substance
Specific heat capacity
(kcal/kg C)
Alcohol
0.58
Ice
0.5
Aluminum
0.22
Iron
0.11
Concrete
0.7
Lead
0.03
Copper
0.093
Mercury
0.033
Glass
0.20
Silver
0.056
Gold
0.030
Steam
0.48
Granite
0.19
Water
1
Human
body
0.83
Wood
0.42
The higher the specific heat of a substance, the more heat it can
absorb and hold.
Example
How much heat must be added to 5 kg of water to increase it
temperature by 20C? The specific heat of water is 1 kcal/kgC.
Answer
Given
mass of water
specific heat of water
change in temperature
m
c
T
5kg
1 kcal/kgC
20C
Find: Amount of Heat (Q)
Solution:
Q = mcT
= 5kg(1kcal/gC)(20C)
= 100kcal
THERMAL EQUILIBRIUM
Thermal Equilibrium occurs when one or more substances reach
a common temperature by exchanging heat. When two substances
are in thermal contact, heat will flow from the hotter substance to the
colder substance until they reach the same temperature and heat will
no longer flow.
Heat lost = Heat gained
Qlost = Qgained
(Eqn 11.9)
For example, if you put ice in warm water, the warm water gets
cold, the ice gets warm, and melts. When the ice completely melts,
they will all have the same temperature. They are in equilibrium.
Example
A 0.5-kg aluminum block at 75C is dropped into a cup of water
with a mass of 2.0 kg at 40C and comes to thermal equilibrium. What is
the final temperature of the water and aluminum? The specific heat of
aluminum is 0.21 kcal/kgC.
Answer
Given
Aluminum Block
mass
specific heat
initial temperature
mAl
cAl
TiAl
0.5-kg
0.21 kcal/kgC
75C
Water
mass
specific heat
initial temperature
mwater
cwater
Tiwater
2.0 kg
1 kcal/kgC
40C
Find:
Final, Equilibrium Temperature (Tf)
Solution
The initial temperature of the aluminum block is greater than the initial temperature of water.
Since heat flow is from hot to cold, then the aluminum block will lose heat, while water will gain heat.
Since the aluminum block will lose heat,
T = (initial temperature – final temperature) = (75C – Tf)
Water will gain heat, so
T = (final temperature – initial temperature) = (Tf – 40C)
Applying the equilibrium condition:
Heat lost by Aluminum = Heat gained by water
mAl x cAl x TAl = mwater x cwater x Twater
Substituting the values,
0.5 kg(0.21 kcal/kgC)(75C – Tf) = 2 kg(1 kcal/kgC)(Tf – 40C)
7.9 – 0.11Tf = 2Tf – 80
Grouping like terms together,
7.9 + 80 = 2Tf + 0.11Tf
88 = 2.1Tf
Tf =
𝟖𝟖
𝟐.𝟏
= 42C
TRANSMISSION OF HEAT
Also known as the movement of heat from the hotter item to
the colder item can be done in any of the following ways: Conduction,
Convection, and Radiation.
CONDUCTION
Conduction occurs when two objects touch. When you place
one end of a bar of metal in the flame of a bunsen burner, heat is
conducted from the end in the flame to the end you are holding.
When two materials are in direct contact, like two parts of the
same metal bar, then conduction can occur. Materials that readily
conduct heat are known as good conductors of heat. Metals are the
best heat conductors. It is easy for atoms or molecules of metal to
transfer their energy to atoms of molecules that are nearby. On the
other hand, there are materials that slow down the conduction of heat,
and those are called insulators. Wood, cork, wool, paper, and
styrofoam are all poor conductors of heat, and therefore good
insulators.
CONVECTION
Convection occurs when the heated substance itself moves.
When the layer of water along the bottom of the spaghetti pot
becomes hot from the stove, this layer of water expands and these
hotter molecules rise letting the cooler water above them move
downward to be heated.
Convection occurs in all unevenly heated liquids and gases,
creating convection currents. Convection currents in our atmosphere
are the main causes of different weather patterns around the world.
RADIATION
Radiation is the only type of heat transfer that can occur in
empty space, such as in outer space. Any energy transferred by this
method is called radiant energy.