Download energy - Earth and Environmental Sciences

Natural Sciences I
lecture 6: Forms of Energy (and related topics)
A brief re-cap...
At the end of the last lecture, we had
arrived at the realization that the kinetic
energy gained by a falling object (in our case
a flower pot) is equivalent to the potential
energy lost during the fall.
KEgained = PElost
KE = ! PE
WORK...
POTENTIAL
ENERGY...
PE = m g h
"#PE = m g #h$
W=Fd
F=mg
d=h
...so W = m g h
KINETIC
ENERGY...
#h
KE = ½ m v2
2
We'll return to this idea of the "equivalence" of
various forms of energy, but first let's make a brief
digression on a closely related matter...
ESCAPE from the Earth: ESCAPE VELOCITY
The question is "To what velocity must on object
be accelerated in order for it to completely escape
Earth's gravity?" The answer to this question has
numerous applications and implications – not only with
regard to launching things into space, but also in
connection with the composition and evolution of the
Earth's atmosphere (the escape velocity question
applies to atoms and molecules as well as to large manmade objects).
This question also involves an interesting confluence of the universal law of gravitation and
the law of conservation of energy. Let's start with gravity, recalling that
F = (G me m) /r
2
Replacing F by mg in accordance with Newton's second law (a = g since we're thinking about the
Earth), we see that
mg = (G me m) / r
2
We also learned that the potential energy of an object in Earth's gravity field is m g h, but h = r
for our present purposes, so
PE = (G me m) / r
The kinetic energy of a on object moving away from the Earth is
KE = ½ m v 2
In order for an object heading away from the Earth to completely escape Earth's gravity, the
rate of loss of kinetic energy cannot exceed the rate of gain in potential energy. In other words,
if the object isn't moving fast enough, it's kinetic energy will be converted entirely into potential
energy before it escapes the Earth's pull. Demonstrating this is cumbersome without recourse to
calculus, but we'll start by writing in symbols what we just stated in words
- #KE / #t = #PE / #t
We have expressions for KE and PE (page 2), so we can plug these in to get
2
- #(½ m v ) / #t = #((G me m) / r ) / #t
Remember our use of the # symbol to convey the change from the initial and final states.
Some of the quantities – m, me, and G – don't change with time, but others do. The initial velocity
we're interested in is the escape velocity ve. The initial distance is the radius of the Earth, re.
The final velocity (vf) can go to zero at infinite time (tf) and infinite distance (rf) from the Earth.
If you plug all this into the equation you'll find that time cancels out and eventually we end up with
an escape velocity of...
sible
respon
T
ve = 2Gme / re
O
N
!
e
You ar he derivation
t
for
The value of ve turns out to be 11.2 km/s.
This insight into escape velocity can be "turned around" to considering objects falling to
Earth. Given what you now know about the acceleration due to gravity and about conservation of
energy, you could probably deduce that a stationary object in space that was "captured" by
Earth's gravity would ultimately hit the Earth at escape velocity with
kinetic energy
2
½ m ve
This is called the accretionary energy. We'll talk more about it later
in the term when we consider the formation of the planets.
Here's a question to ponder: Why are satellites launched on
rockets rather than shot into orbit with big guns? Wouldn't it
be simpler just to fire them off as un-powered projectiles?
3
4
Let's look at a
more familiar example
of the inter-conversion
of kinetic and potential
energy – the swinging
of a pendulum. The
initial lifting the
weight in Earth's gravity field involves the
performance of work,
which imparts potential
energy to the weight:
W =Fd
=mgh
PE = m g h
100% PE
0% KE
h
reference height
ai
f ri r re
ct sis
io ta
n
ne nce
gl a
ec nd
te
d
Energy Conversion
As the weight falls
PE = 0
2
KE = ½ m v
0% PE
100% KE
PE = (m g h) / 2
2
KE = ½ m v
50% PE
50% KE
PElost = KEgained
At the bottom of the swing, the velocity is at a maximum
m g h = ½ m vmax
2
½
vmax = (2gh)
This equation conveys a very general conclusion: i.e., that the final (maximum) speed of a
falling object – at the point where all of its initial potential energy has been converted to kinetic
energy – is related in a simple way to the initial height and the gravitational constant. This final
speed is independent of the mass of the object (which Galileo knew ~400 years ago!).
5
Some final thoughts on WORK and ENERGY...
By now the connection between work and energy should be coming into focus. We learned
that work (F x d ) can create potential energy, as in the raising of an object in a gravitational
field. Work can also impart kinetic energy to an object by accelerating it. A good way to bring
this all together is to recognize that the force applied in doing work goes into overcoming a
resistance, which causes a change in energy...
resistances
4
inertia
fundamental forces (gravitational, magnetic, etc.)
friction
shape (e.g., of a spring or other deformable object)
energy change produced by overcoming resistance
1 inertia
2 gravity
3 friction
4 shape
increase in KE
increase in PE
increase in temperature (heat)
increase in PE
3
Some examples from sports...
1
(new olympic sport?:
dragging a weight
along the highway)
2
In all of these examples, the work done
produces an increase in the energy of the
object, which could in turn be used to do
work on other objects.
We saw on page 4 that a pendulum is really just a device for continuous inter-conversion of
potential energy and kinetic energy (it would perform this function perpetually if not for the
effects of friction).
Kinetic and potential energy are not the only forms of energy, and all others can be converted
from one form to another as well. What are some other forms of energy?
Mechanical Energy
Involves familiar machines, systems and objects in various ways...
kinetic energy of a moving object
potential energy of
water behind a dam
energy stored in a spinning flywheel
Pgas = 2,000 psi
potential energy of
compressed spring
potential energy
of compressed gas
Chemical Energy
Energy involved in chemical reactions or stored in chemical bonds
Examples: petroleum products, coal, wood, food, explosives, phase change materials, etc.
Oxidation is often involved, e.g...
wood + oxygen = carbon dioxide + water + energy
reactants
products
6
7
Radiant Energy
Visible and infrared light (heat), radio waves, etc. – travels through space.
Example...
HOT
COLD
Electromagnetic spectrum
gamma X-rays
rays
Electrical Energy
UV
Energy carried by electric current...
(-)
(+)
e
e
!
e
!
e
!
e
!
!
visible IR
micro - TV FM AM
waves
radio
8
Energy Conversion and Conservation
We saw in the case of the swinging pendulum that energy can be readily converted from one
form to another – in that case, the conversion was between the kinetic energy of the moving
weight and the potential energy the weight attained by virtue of its position in the Earth's
gravity field. All the forms of energy discussed above can also be converted from one into
another. During a conversion, energy is conserved. These observations amount to the Law of
Conservation of Energy:
Energy cannot be created or destroyed but it can be converted
from one form to another, and is conserved during the process.
Question: What energy conversions take place as an automobile speeds down the highway?
Sun's rays heat
car (radiant
energy to heat)
air set in
motion by
moving car
Question: Which of the
energy conversions we
have identified (or any
additional ones you
might find) involve the
performance of WORK?
tires:
mechanical energy
(rotation) into
mechanical energy
(forward motion)
mechanical energy
into heat
engine:
chemical energy
into mechanical
energy (kinetic)
mechanical
energyinto heat
(friction)
chemical energy
into heat
heat into radiant
energy
heat into radiant
energy
others?...
9
Nuclear Energy
Energy released by fission or fusion of atomic nuclei (this involves conversion of matter into
energy)
fission of uranium or plutonium
E = m c2
fusion of hydrogen (future?)
Nuclear reactions involve reactants
and products just as chemical reactions
do; e.g.
Summing the masses of reactants and products...
238.0003 u
233.9942 u + 4.0015 u
233.9942 + 4.0015 - 238.0003 = -0.0046 u
238
U
92
234
Th
90
4
+ 2 He
...so we've lost some mass in this nuclear reaction.
This mass was converted to energy.
E = m c2
This reaction describes the initial a decay
of the naturally radioactive isotope
uranium-238. It is an example of a massto-energy conversion.
(See p. 73 of your text)
#E = #m c 2
In the above example, #m = -0.0046 u.
10
Additional thoughts on Energy
Conversion
The main conclusion of the
preceding pages is that any form of
energy can be converted into any
other form. Energy conversion goes
on around us all the time – indeed, it
is vital to the functioning of society
and to all of our individual lives. On a
grander scale, energy conversion is an
integral part of the Earth's
biological, geological and
environmental systems at all levels
(and through all time). Nature has
her own mechanisms and pathways for
energy conversion, which are covered
in some detail in Natural Sciences II.
Here are some that go on around us
all the time...
device or
organism
conversion
green plants
radiant (light) to chemical
animals
chemical (food) to heat and motion
auto engine
chemical to kinetic
auto brakes
mechanical to heat
elevator
electrical to potential
lightbulb
electrical to radiant (light)
electric stove
electrical to heat
gas stove
chemical to heat
electric generator
mechanical to electric
nuclear reactor
matter to heat
Corollary to the Energy Conservation Law:
The efficiency of energy conversion is a measure
of how much of the converted energy ends up in
the desired form
A final question: Does
the existence of nuclear
energy contradict the
law of conservation of
energy?