1 Energy
1
1.1 What is energy?
Energy is a difficult concept, you can’t see it or hold it,
but it is fundamental to life.
You may have heard of the principle of conservation of
energy: Energy cannot be created or destroyed, only
converted from one form to another.
So rather than looking at what energy is, we can look
at its different forms, properties and effects.
Table 1:
Forms of energy
chemical energy: energy released in a chemical
reaction eg from the food we eat; petrol we put in our
cars; energy stored in a battery
mechanical energy:
either potential energy (PE): energy stored due to
position eg a compressed spring (elastic PE); a pencil
held above the floor (gravitational PE)
or kinetic energy (KE): energy of a moving object eg a
moving car
sound energy: eg musical instrument, engine noise,
speech, thunder, diagnostic ultrasound, SONAR
electrical energy: electrical potential energy
associated with the field around an electrical charge
thermal energy: the energy of a hot object
nuclear energy: energy released when mass is
converted to energy eg the fission (splitting) of a
nucleus in a nuclear reactor
electromagnetic energy: the energy carried in
radiowaves, microwaves, infrared, visible light,
ultraviolet, x and (gamma) rays.
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1.2
Energy conversions
Remember, energy cannot be converted or destroyed,
only converted from one form to another.
PICK UP A PENCIL OR SIMILAR OBJECT AND HOLD IT IN
THE AIR, ABOVE A TABLE. NOW DROP IT.
WHAT HAPPENED TO THE PENCIL?
It fell out of your fingers, travelled through the air and
hit the table with a pencilly noise.
WHAT HAPPENED TO THE PENCIL IN TERMS OF ENERGY?
While you were holding it in the air, it had potential
energy because you lifted it up against the force of
acceleration due to gravity. When you let go, this
potential energy was converted into kinetic energy as
the pencil accelerated through the air. When it landed
on the table, the kinetic energy was converted into
sound energy. As the sound fades, its energy is being
converted into thermal energy of the air and the
ground.
Q1 CONSIDER ...
WHAT WOULD HAVE HAPPENED TO
THE KINETIC ENERGY IF THE PENCIL HAD LANDED ON
CARPET? See page 7 for suggested answer
Let’s think about what happens when you go out for a
drive in your car.
You put petrol in the tank: the petrol is ignited by a
spark from the plug and the gas formed expands to
push the piston down and turn the crankshaft. This
movement is transferred to the driveshaft and the
wheels to move the car. The engine gets hot. The
crankshaft also drives an alternator which charges the
battery, runs the lights, windscreen wipers, radio.
3
Q2 INTO WHAT FORMS OF ENERGY HAS THE
CHEMICAL ENERGY OF THE PETROL BEEN CONVERTED?
See page 7 for suggested answer
x-ray tube
If we could measure and add up all this energy, we
would find that the energy input in the form of chemical
energy from the petrol equals the energy output in its
various forms. So energy has not been created or
destroyed, only converted from one form to another.
The x-ray tube is another example where energy is
converted from one form (electrical) into other forms
(x-rays, heat, light).
An ultrasound transducer converts electrical energy
into sound energy, and reflected sound energy back
into electrical energy.
1.3
How do we measure energy?
Energy is measured in SI units called joules (J).
Look on the back of a packet of crisps:
If you don’t understand
the use of prefixes such
as k for kilo, see
section 5
On this packet, Energy per 24g bag is 484 kJ
= 484 000 J
4
(Open University, 1979)
1 x 1020 J
severe earthquake
1 x 1019 J explosion of a hydrogen bomb
1 x 1018 J
1 x 1017 J
1 x 1016 J
1 x 1015 J
1 x 1014 J
1 x 1013 J
1 x 1012 J Concorde flying from London to New York
1 x 1011 J
1 x 1010 J
1 x 109 J
1 x 108 J
combustion of one gallon of petrol
1 x 107 J
If you are not happy
with the use of powers
of ten as shown in this
table, you should refer
to section 5
1 x 106 J
running an electric fire for one hour
5
1 x 10 J
1 x 104 J
car moving at 30 mph
1 x 103 J
1 x 102 J
1 x 101 J
lifting 3 kg bag of potatoes to waist height
1J
its
stretching a 10 cm rubber band to three times
natural length
1 x 10 J visible light from a light bulb in one second
-1
1 x 10-2 J
1 x 10-3 J
1 x 10-4 J
1 x 10-5 J
adult talking for one second
-6
1 x 10 J
1 x 10-7 J
1 x 10-8 J
1 x 10-9 J
1 x 10-10 J
Table 2:
How
much
energy is a
joule?
1 x 10-11 J
5
measured in units of electronvolts (eV).
1 eV = 1.6 x 10-19 J.
Electronvolts are used for the energy associated with
atoms and widely used in radiography.
A typical x-ray photon has an energy of 70 keV.
If you are unsure of
using powers of ten
and entering these
values into a calculator,
see
section 5
Q3
HOW MANY JOULES OF ENERGY IS A TYPICAL 70
KEV X- RAY PHOTON?
See page 7 for answer
So one x-ray photon carries less energy than someone
speaking for 1 second! But there are millions of x-ray
photons in a beam of x-rays.
1.4
Mass-Energy Equivalence
Einstein’s theory of relativity proposed if an object
gains energy, its mass increases and similarly mass
decreases with a loss of energy.
Mass and energy are linked by
E = mc2
where E is energy in joules, m is mass in kilograms
and c is the velocity of light, 3 x 108 m s-1 (metres per
second)
linear accelerator
This increase/decrease in mass is not obvious in
everyday situations, but can be seen at the atomic
level, following nuclear fission for example. It is also
apparent when an electron is accelerated in a linear
accelerator, such as used for radiotherapy.
Q4
See section 5
THE MASS OF AN ELECTRON IS 9.1 X 10-31 KG. USE
THE FORMULA ABOVE TO WORK OUT THE ENERGY
EQUIVALENCE OF ONE ELECTRON, IN BOTH JOULES AND
ELECTRONVOLTS.
See page 7 for answer.
The
electronvolt
Energy may
also be
6
Waves transfer energy from one point to another.
Waves in water for example, can carry enough energy
to knock someone over, or destroy sea walls.
Electromagnetic waves, such as radio waves, are
radiated into space by oscillating charged particles.
Radio waves transfer sound energy from a transmitter
to a receiver (your radio).
X-rays transfer energy from an x-ray tube to the patient
and a detector, such as x-ray film, behind the patient.
Thermal energy is transferred from the sun, through
space, to the Earth.
Such waves are transverse waves, where the particles
vibrate at right-angles to the direction of travel.
Longitudinal waves are produced from vibrations in the
same direction as the wave, giving waves of
compression and rarefaction. Sound waves are
longitudinal.
A wave can be described in terms of its wavelength,
frequency, period, velocity and amplitude.
Waveform of
transverse wave:
intensity (I) plotted
against time (t)
1.5
Wave
s
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Wave characteristics
One cycle is one complete waveform, from one point to
the same point again.
The wavelength is the distance travelled in one cycle
(in metres, m)
The frequency is the number of cycles per second (in
hertz, Hz)
The velocity is its speed: in a vacuum,
electromagnetic waves travel at the velocity of light: 3
x 108 m s-1.
The velocity of soundwaves varies, depending on the
medium: in air, soundwaves travel at 330 m s-1, in
water at 1540 m s-1.
The amplitude is the magnitude of the peak of the
waveform.
Indicate on the wave above:
one cycle
one wavelength
the amplitude
The velocity (v) of the wave is related to its frequency
(f) and wavelength ( ):
This formula can
be used to
calculate one
characteristic of a
wave, when the
other two are
known.
v =
f
For example, the wavelength of blue light in the
electromagnetic spectrum, is approximately 400 nm.
In a vacuum, the velocity of all electromagnetic
radiation is 3 x 108 m s-1.
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So the frequency of blue light
You should notice
that as
wavelength
increases (gets
longer), frequency
decreases
3 x 108
400 x 10-9
=
v =
=
7.5 x 1014 Hz
Q5
Try this:
WHAT IS THE FREQUENCY OF RED LIGHT,
OF WAVELENGTH 800 nm?
.
The frequency of x-rays is very high, so the wavelength
is very short, less than 10 nm. This means x-rays tend
to behave more like particles than waves. These
particles are known as photons, or quanta, from the
term quantum physics.
The energy of a photon, E is related to the frequency,
f, of the wave:
Where h is
Planck’s
constant (6.62 x
10 –34 J s)
E
=
hf
From the first equation, f = v
and can be substituted into the second to give
E
=
hv
Q6
YOU SHOULD NOW BE ABLE TO CALCULATE
THE WAVELENGTH OF A TYPICAL 70 KEV X-RAY
PHOTON. BUT REMEMBER, THE SI UNIT OF
ENERGY IS THE JOULE … SEE SECTION 1.3 HOW
DO WE MEASURE ENERGY?
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given in table 1
describe energy conversions in everyday situations
state the SI unit of energy
convert electronvolts into joules
state Einstein’s theory of relativity and give the
formula relating mass and energy
describe the main characteristics of waves
use the formula v = f
1.6
Answers to questions
Your answers to questions 1 and 2 should be similar to
these:
Q1: The kinetic energy of the pencil would have been
converted into some sound energy, some kinetic
energy of the carpet fibres and some heat energy.
Q2: The chemical energy of the petrol was converted
into:
kinetic energy
movement of crankshaft
thermal energy
heat of engine
electrical energy
alternator
chemical energy
battery
sound energy
radio, horn
electromagnetic energy
headlights etc
Q3: an x-ray photon of 70 keV = 70 x 103 eV
(or
70 000 eV)
multiplied by 1.6 x 10-19 gives 1.12 x 10-14 J
Q4:
/ means divided by
E
=
mc2
=
9.1 X 10-31 x (3 x 108)2
=
8.19 x 10-14 J
=
8.19 x 10-14/1.6 x 10-19 eV
=
511875 eV
or approximately 511 keV
Q5: f = 3 x 108/800 x 10-9 = 3.75 x 1014 Hz
1.5 Check
that you
can:
Q6:
= (6.62x10-34 x 3x108)/70x103 x 1.6x10-19
= 1.77 x 10-11 m
outline the
various
forms of
energy as
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