Temperature, Heat and Heat Transfer
When we think of temperature, we usually think of
something that we measure with a thermometer. However,
have you ever stopped to think about what you were
measuring?
Temperature is a measure of the kinetic energy of
molecules and atoms in the surroundings. An environment
where the molecules are moving around very quickly is
said to have a high temperature. An environment where
there is relatively small motion has a low temperature.
This is how the Kelvin temperature scale was
determined. We hopefully are familiar with the Celsius and
Fahrenheit scales:
Water boils:
100 degrees Celsius
212 degrees Fahrenheit
Water freezes:
0 degrees Celsius
32 degrees Fahrenheit
and 1 degree Celsius is 9/5 degrees Fahrenheit. So we
can go back and forth between units of temperature. In
equation form:
TF = 9/5 TC + 32
Furthermore, as you can tell from the units of division, we
will stick with the Celsius scale.
The Absolute Temperature Scale
The Kelvin scale was defined from the concept of
absolute zero. Absolute zero is the theoretical point where
all molecular and atomic motion stop (However, when you
encounter quantum mechanics next semester you will find
out that there is always some residual energy left over, this
is known as the zero-point energy). It was found by
looking at how the pressure in a gas reacts to falling
temperature:
The hypothetical negative pressure region cannot
happen so there is a limit to how “cold” something can get.
It was found to be –273 degrees Celsius. This was the 0
point for the Kelvin scale.
So to find a temperature in Kelvin, you just add 273
degrees to the Celsius scale. Therefore:
Water boils:
Water freezes:
373 Kelvin
273 Kelvin
Notice not “degrees” Kelvin!
The Celsius, Fahrenheit and Kelvin scales were all
named after the men who “discovered” them: Anders
Celsius (1701-1744), Gabriel Fahrenheit (1686-1736), and
Lord Kelvin (1824-1907), respectively.
Temperature and Solids
In prior classes, you should have investigated the
physics of solids and how they shear or stress when a force
is applied to them. One other property of solids is that
temperature also affects their shape.
We then have an equation similar to the Young’s
modulus equation that illustrates how much an object will
“stretch” under certain temperature conditions:
L = LoT
where  is called the coefficient of linear expansion
and like Young’s modulus, has a separate value for every
different type of material.
What are its units?
Furthermore, if you do not take this expansion into
account when you are building bridges, sidewalks, railroad
tracks, you will have a lot of problems!
As you can imagine there is also a relationship for a
volume expansion:
V = VoT
The only substance that does not follow the rule is
water. When water is cooled, it actually expands!
Therefore, its density decreases and it is able to float. So
fish and other sea life are safe below.
Table 19.2 has values for the coefficients of linear and
volume expansion for several different materials.
Heat and Internal Energy
When one thinks of temperature, they usually think of
the word heat. However, like most physics terms, it has
been misused and not understood.
Formally:
Heat is energy that flows from a higher-temperature
object to a lower-temperature object because of the
difference is temperature.
If heat is the flow of energy, what are its units?
Furthermore, different amounts of heat are needed to
increase the temperature of different object. How much
heat is needed is given as:
Q = cmT
Where c is known as the specific heat capacity of the
substance. Every different substance has a different heat
capacity. Next week you will investigate this for yourself.
Finally, what are the units on specific heat?
There is an analogous measure of heat other than a
Joule. It is called the calorie. By definition, a calorie was
defined as the amount of energy transfer needed to raise the
temperature of 1g of water from 14.5 degrees Celsius to
15.5 degrees Celsius. The English unit of heat is called the
British Thermal Unit (btu’s) which is defined as the amount
of heat needed to raise one pound of water from 63 to 64
degrees Farhenheit.
Joule himself performed one of the more important
experiments done on the transfer of energy and its
equivalent amount of heat. He set up an experiment where
2 blocks fell from a height h. By varying the conditions of
the experiment, he noticed that the loss of mechanical
energy, 2mgh, was proportional to the increase in water
temperature T. The proportionality constant had a value
of 4.18 J/g C. Hence, 4.18 J of mechanical energy raised
the temperature of 1 g of water 1 degree Celsius.
Therefore:
1 cal = 4.186 Joules
1 kcal = 1 Cal = 4186 Joules
This equality is known, purely for historical reasons as
the mechanical equivalent of heat.
Specific Heat and Latent Heat
The process to try and measure the specific heat of a
substance is called calorimetry. The process of
calorimetry is relatively straightforward.
You start with a calorimeter of a known substance,
usually aluminum and water. You then add a substance
you want to find the specific heat of. You know how much
heat will go into heating the water and aluminum so then
you can measure the specific heat of the substance:
The specific heats of several different substances are
given in table 20.1.
Surprisingly, there are situations where the addition of
heat does not cause a change in temperature. Instead
something a little different happens. You are familiar with
this if you ever had a glass of water with ice.
The ice water is at a temperature close to 0 degrees
Celsius. As heat is added to the system, the ice begins to
melt but the temperature of the water does not increase.
When a substance changes from one “phase” to
another, the amount of heat that must be added or removed
depends on the type of material and the nature of the phase
change. The heat per kilogram associated with a phase
change is called the latent heat.
The amount of heat need is then :
Q = mLf (Lv)
Table 20.2 contains values of the latent heat of fusion
and the latent heat of vaporization of several different
substances. It also includes the melting and boiling points
these substances as well. For example:
Substance
Helium
Oxygen
Water
Lead
Aluminum
Melting Point
-269.65
-218.79
0
327.3
660
Boiling Point
-268.93
-182.97
100
1750
2450
We can do an example to help illustrate this point:
What mass of steam initially at 130 degrees Celsius is
needed to warm 200 g of water in a 100 g glass container
from 20 to 50 degrees Celsius?
You will often see negative (-) signs when looking at
sample problems in the book. They are used to keep track
of heat lost or gained…you really do not need them but
don’t get lost in the algebra.
The Transfer of Heat
We will discuss three ways to transfer energy from
one place to another.
One way to transfer heat is called convection.
Convection is the process in which heat is carried from
place to place by the bulk movement of a fluid.
There are many examples of convection in our
everyday experiences including boiling water, “heat” rising
in a house and solar granulation !
Another way to transfer energy is called conduction
and you experience this whenever you place an aluminum
baseball bat into a fireplace.
Conduction is the process whereby energy is
transferred directly through a material as an exchange of
kinetic energy between subatomic particles. The bulk
motion of the material plays no part in the transfer.
How much energy can be transferred from one place
to another depends on several things; the type of material,
the mass, the cross-sectional area are a few of them.
Quantitatively:
Q = (kA t)|T/x|
Where k is called the thermal conductivity of the
material. Table 20.3 has values of k for several different
materials.
If we divide through by the change in time, we have
units of J/s which you should recognize at a unit of power –
Watts. Therefore, we can also write the law of thermal
conduction as:
P = kA |T/x|
And |T/x| is called the temperature gradient.
From an engineering standpoint, the value of x/k is
referred to as the R value of the material. The higher the R
value the energy lost through the material is much lower.
That is why in constructing a house, the type of insulation
used is very important in determining whether the house
will be energy efficient. You can also see that if the
temperature gradient is very large, say in the winter or
summer, the heat lost through the walls will be very large
regardless the insulation you have!
Finally, the third means of transporting energy is by
radiation, all objects radiate energy in the form of
electromagnetic radiation produced by the thermal
vibrations of the molecules.
The rate at which an object radiates is proportional to
the fourth power of its absolute temperature. The is known
as Stefan – Boltzmann’s law and quantitatively is given as:
P = AeT4
Where  is called Stefan-Boltzmann’s constant and e
is called the emissivity constant.
When an object is in equilibrium with its
surroundings, it radiates and absorbs energy at the same
rate, and so its temperature remains constant. An ideal
absorber is defined as an object that absorbs all energy
incident on it, or e=1. Such an object is called a
blackbody. In contrast, an object where e=0, is an ideal
reflector.
Now, why can the machines in the MATRIX, utilize
the heat lost by humans?
How much heat is lost in 1hr through our bodies at 35
degrees Celsius into the room at 20 degrees celcius?
Assume e=0.9 and A=1.5 m2.