FORMS OF ENERGY
FORMS OF ENERGY CONTENT OVERVIEW
This unit began by stating that an object or system can be said to have energy if the object or
system might cause changes to occur. As these changes occur, energy can be transformed from
one form to another. For example, you have seen how stored internal energy (potential energy) can
be transformed into thermal energy (as in the heat packs) or from thermal energy to internal energy
(as when ice was induced to melt by adding salt).
The principle of conservation of energy is one of the most important concepts in all of science.
What really makes this principle powerful is when you have the ability to measure energy in its
different forms. The standard unit for measuring energy is the Joule (abbreviated J). Another unit
for energy is the food Calorie. If you read on a box of food the Calorie content of a serving of the
food, then you know how much energy the food can release in your body. (The Calorie content is
not the total energy, though. It is only the chemical potential energy that can be released when the
food is digested. A glass of water, for example, possesses internal energy even though it contains
no food Calories.)
A Calorie is equal to the amount of heat needed to raise the temperature of 1 kg of pure water
by 1 degree Celsius. (The amount of heat needed to raise water one degree is almost independent
of the starting temperature of the water.) Numerically, one Food Calorie is approximately 4,184
Joules. Sometimes a unit called the calorie (with a little “c”) which is 1/1,000 of a food Calorie is
also used. Thus, 1 food Calorie is actually equal to 1 kilocalorie). 1 calorie is equal to the amount
of energy needed to raise the temperature of one gram of water by 1 degree Celsius, and it equals
4.184 Joules. Most science books are very careful about using capital C when dealing with food
Calories, but cereal boxes and so forth generally are not. Keep in mind, therefore, that the
“calorie” listed on a package of food really represents a kilocalorie (1 Calorie).
Another unit that is often encountered in discussions of energy usage is the Watt. By
definition, 1 Watt = 1 Joule/sec. Watts are used when you want to discuss the rate of energy
usage. The Watt is actually a unit of power, which is the rate at which energy is used. Think, for
example of light bulbs or stereo speakers. A 100 W light bulb is brighter than a 60 W bulb, and it
uses energy at a faster rate than a 60 W bulb. In fact, a 100-W lightbulb uses 100 J of electrical
energy per second, while a 60 W lightbulb uses 60 J of electrical energy per second.
There is one more unit that should be mentioned. Electric bills from utility companies usually
tally the energy used in terms of “kw hr” or “kilowatt hours.” What is a kilowatt hour? Imagine
using energy at a rate of 1,000 Watts for one hour (imagine, for example, ten 100-W lightbulbs).
The total energy used is one kilowatt hour. A single 100-W lightbulb needs to burn for 10 hours
to use 1 kw hr.
ENERGY FORMS
All of the different forms of energy in the macroscopic world can be traced down to the particle
level and classified as either kinetic energy or potential energy of the particles. Kinetic energy
refers to the energy due to the motion of a particle. Potential energy refers to the energy related to
the position of a particle relative to other particles. Several of the more familiar forms of energy are
described below.
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Kinetic Energy
An object which is moving from one place to another is said to have translational kinetic
energy. The translational kinetic energy of an object is given by
KE =
1
2
m v2
where m is the mass of the object (in kilograms) and v is the speed (in meters/second) at which the
object is moving. This formula applies to macroscopic object such as the earth in its orbit around
the sun and to microscopic particles like atoms.
Example: What is the kinetic energy of a 2 kg particle traveling at speed 3 m/s?
Answer: For this particle, m = 2 kg and v = 3 m/s. Using the above equation for kinetic energy
you obtain
KE = (1/2) (2 kg) (3 m/s)2 = (1/2) (2) (9 ) kg m2/s2 = 9 J.
One thing that this example illustrates is that the unit of energy, the Joule, is related to the units for
mass, length, and time: 1 Joule = 1 kg m2/s2.
It is probably worth noting explicitly that the kinetic energy of an object depends on both its
mass and its speed, but in slightly different ways. Since K.E. is proportional to the mass m,
doubling the mass doubles the kinetic energy. But since K.E. is proportional to the square of the
speed v, doubling the speed increases the energy by a factor of 2 “squared” or 4. So, as a
practical example, when you are driving in your car at 60 mi/hr you have 4 times as much kinetic
energy as when you are driving at 30 mi/hr. There are several implications of this fact. For
example, it means that the person driving at 60 mi/hr has four times as much energy to lose in order
to stop, and therefore four times as much thermal energy will be generated as the car stops. This
person will also need four times as much distance in order to sop. (Recall the activity of rolling
marbles into cups.) Also, if you accelerate your car from 0 to 60 mi/hr by giving your car energy at
a constant rate (which is approximately what happens if you hold the accelerator pedal at a constant
position), it takes four times longer to reach 60 mi/hr from rest than it does to reach 30 mi/hr.
An object which is spinning is said to have rotational kinetic energy. A ball rolling along the
ground would therefore have both translational kinetic energy (because it is moving) and rotational
kinetic energy (because the ball spins as it rolls). The exact amount of rotational kinetic energy of
an object depends on the mass, the shape, and the speed of rotation of the object.
Potential Energy
There are several forms of potential energy. One important form of potential energy is
gravitational potential energy. As the name implies, this potential energy arises from gravitational
interaction. In our everyday experiences this potential energy arises from gravitational interactions
between objects and the earth. An object has a greater potential energy at higher altitudes than at
lower altitudes. Also, the more mass an object has the more gravitational potential energy there is.
Recall the marbles rolled down the rulers: the higher a marble was above the tabletop, the greater
was its energy and the further it could push the inverted cup. Similarly, for a given height, the
greater the mass of the marble, the further it could push the cup. Mathematically, you can write
gravitational potential energy (GPE) as GPE = m h g, where m is the mass of the object, h is the
height or altitude of the object, and g is a constant equal to 9.8 meters/second2 and is called the
acceleration due to gravity. The value of g would be different if you were not on the surface of the
earth.
An alert reader may be wondering about the altitude h. What are you supposed to measure the
altitude from? Do you want height about sea level? the floor? a table top? or what? The answer is
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“any of the above.” Gravitational potential energy becomes a valuable concept when we think
about how it changes when an object’s position changes. If you are doing an experiment above say
a tabletop (remember the marble experiment) then you probably are most interested in knowing
how an object’s potential energy is different from what it would be right on the table, and you can
just let h be the height of the object above the table. If you are doing an experiment by dropping an
object down a deep hole, then you would probably want to measure h relative to the bottom of the
hole.
Other forms of potential energy frequently encountered include the following:
Electric potential energy refers to the energy of electric charges due to their interactions with
other charges. We’ll study electrical interactions later.
Chemical potential energy refers to the energy due to the interactions of atoms involved in
forming molecules. (This energy is due to the electric potential energies of the charges in the
atoms.)
Nuclear potential energy refers to energy in the form of mass stored in the nuclei of atoms.
Thermal Energy
Within any system or within any object made up of smaller particles, there will be individual
motions of the constituent particles. The temperature of a system is a measure of the average
translational kinetic energy of the individual particles in their random motions within the system.
Since the standard unit for measuring energy in the metric system is the Joule, temperature could be
measured in Joules. It will be shown below that the average kinetic energy of air molecules in a
room at 23 °C is 2.72 x 10-21 Joules. So, if you really wanted to, you could say that the temperature
of the room was 2.72 x 10-21 Joules. However, you will probably agree that specifying temperature
in this way would not be particularly practical. So instead temperatures are usually converted to
Kelvins or degrees Celsius (or degrees Fahrenheit by some Americans), and we must simply
remember that temperature is measuring the average kinetic energy per particle.
The relationship between the temperature (in Kelvins) of a substance and the translational
kinetic energy of the particles making up the substance is as follows:
(KE) =
3
2
k T
where k is a numerical constant, called Boltzmann’s constant, given to 5 digits by
k = 1.3806 x 10-23 Joules/Kelvin.
and T is temperature in Kelvins. (0 °C = 273 Kelvins.) If all of the particles in a substance
completely stopped moving (which can not ever be completely accomplished), then the average
translational kinetic energies of the particles would be equal to zero, and the temperature would be
absolute zero = 0 Kelvin = -273 °C.
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Example: What is the average kinetic energy of air molecules in a room at 23 °C?
First, we you convert the temperature from Celsius to Kelvin:
T = 273 K + 23 K = 296 K.
Then you can calculate the kinetic energy as
3
K.E. = 2 (1.3806 x 10-23 J/K) (296 K) = 6.12 x 10-21 J.
This answer is not a very large number, but because a molecule is so light, it corresponds to a very
large velocity. For example, a water molecule has a mass of approximately m = 2.99 x 10-26 kg.
Solving K.E. =
v =
1
2
mv2 for v gives
2 K.E.
m
=
2 (6 . 12 x 10− 21 J
2 . 99 x 10− 26 kg
= 640 m / s.
(The units have come out in meters per second because we have used standard metric units.)
Each moving particle possesses kinetic energy. The sum of these kinetic energies is the total
kinetic energy within the gas..
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