| Energy is the capacity to do work or to transfer heat |
Work is the product of force
and distance. For example, a force of 40 pounds moving 15 feet represents
600 ft-lbs of energy. This mechanical aspect of energy is manifested in
many activities. Think of the motion of an automobile, a cheetah, or a rocket.
The “Big Three” of engines
-- gasoline, diesel, and steam turbine have carried economies from the industrial
revolution to the modern era. All three are heat engines -- they transform
heat, or thermal energy to mechanical energy.
| In the other
direction, mechanical energy can be dissipated or degraded to heat,
as with brakes on an automobile. All forms of energy - even light,
sound, and the biochemical energy in food - are ultimately dissipated
as heat. The heat equivalent of non-thermal forms of energy is found by various methods. A laboratory approach calculates the energy in an egg, for example, by putting it in a bomb calorimeter and reducing it to ash. The the difference between the Calories in and the Calories out is contributed by the egg -- about 150 Calories. Sterile factory egg or fertilized chicken, each is assigned the same number of Calories |
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2. Work and Power Lifting 200 pounds two feet is a challenge for most of us. On the other hand, almost anyone can pull a rope with 40 pounds (#) of resistance for 10 feet. Yet, from the view-point of output, both accomplish equal amounts of gravitational work, 400 foot-pounds: 200 lbs x 2 ft = 400 ft-lbs or 40 lbs x 10 ft = 400 ft-lbs.
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Figure 7-2
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Exercise
7.1 You climb a ten-foot flight of stairs. How much
work is done on your body?
Exercise 7.2 A canoeist
makes 150 one-yard strokes. The force averages 40 lbs over each stroke.
How much work has the paddling done?
Exercise 7.3 A student working
in the library shelves 450 books from a cart. On the average, a book weighs
ten pounds and is lifted four feet above the cart. How much shelving work
has been done?
Notice that nothing was said about the
time it takes to do work in the above examples or exercises. Everyday
speech recognizes that the faster we go up steps the more power it takes.
We recognize that someone who accomplishes many tasks in a short time
exhibits power.
| Power is energy flow -- it is the change in energy per unit change time. |
Exercise 7.4 If you climb a flight of stairs in 20 seconds, what is the power output?
Exercise 7.5 The canoe paddler in Exercise 2 does the 150 strokes in five minutes. What is the power output?
Exercise 7.6 The student assistant in Exercise 30 minutes to shelve the books. What is the power output?
Exercise 7.7 Can you explain why the energy outputs for paddling (Ex.5) and shelving (Ex.6) are the same, yet the power outputs are very different?
Exercise 7.8 Electricity always seems to elicit such terms as power lines, power outages or power usage. Power is measured in kilowatts. However, electric bills are based on how much energy is consumed. What units of energy do utility companies use? (If you have trouble with this one, take a look at an electric bill. As a last resort, call the local electric company!)
3. Thermal Energy One measure of heat energy is the BTU
(British Thermal Unit). A BTU is the energy that goes into heating one pound
of water one degree Fahrenheit. Amazingly, this is the equivalent of 778
ft-lbs of work. In other words, the thermal energy that goes into raising
the temperature of an 11 ounce mug of coffee one degree (°F) is approximately equivalent
to the work of lifting 55 pounds up one flight of stairs. (A pint , or 16
fluid ounces of water weighs about one pound. Rule of thumb -- A
pint’s a pound the world around.)
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Figure 7-3 |
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There are a seemingly endless
number of energy units and their conversions, with contributions from the
English and French systems, as well as heat and mechanics. The BTU and ft-lb,
for example, are from the English system. The end of this chapter has a
list of energy units, as well as an extensive conversion table.
Exercise 7.9 Approximately
how many foot-pounds is the equivalent of raising the tempera-ture of a
pint of tea from 70 to 110 degrees (°F)
Exercise 7.10 . . .
4. Conservation of Energy Here is a fundamental principle
of physics, known as the First Law of Thermodynamics --
| Energy can neither be created nor destroyed, it can only be transformed. |
In a closed system or tank, the energy remains constant. (See Fig. 7-4.) If the energy at the start is Q0, then it remains at Q0. In an open system, if the storage does not change, the ingoing and outgoing energy must be equal. If the storage changes, this must be reflected in the energy balance.
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| Figure
7-4 Energy conservation law |
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The
energy input to a system might not balance the energy that goes out,
as in Fig. 7-5. In the system on the left, the input is 75 units
of energy but only 60 units go out. Since the First Law requires
that the energy be conserved, system had to gain 15 units of
energy. (The energy units could be Cal, BTU, kw-hr -- whatever fits
the context.) In the right system the input is short 15 units
of energy so we can infer that the system must have lost 15 units.
The sinks are depositories of leakage
or rejected energy. It is usually low-grade heat, as in respiration,
an engine exhaust, or a non-insulated hot water heater. The outputs
represent useful work. Examples of this are plant growth , walking or
the execution of a work of art.
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| Figure
7-5 Energy conservation law |
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Exercise
7.11 Suppose the input to a system is 120 Cal,
it outputs 15 Cal as work, and 85 Cal are lost to the sink. What happened
to the missing Calories? (Draw a picture!)
Exercise 7.12 In Ex.
1, suppose that 110 Cal end in the sink. What about the extra Calories?
5. Entropy and the Degradation of Energy In any transformation
of energy some becomes unavailable. Entropy is a measure of its
unavailability. This loss of usable energy is due to many causes --
· In mechanical systems it is friction
· In electrical systems it is resistance
· In fluid systems it is turbulence, viscosity or mixing
· In communication systems it is noise
· In an agency it is disorganization
Anything that tends to degrade, disorder, or destruct a system will
increase the entropy of the system. The above examples and terminology
emphasize physical systems.
In living systems, entropy can be
increased in various ways --
· An organism becomes sick, injured or lost
· A business is pilfered, has a strike, or is overtaxed
· A society becomes disorganized or loses direction
A decrease in entropy is associated
with the opposite of the above attributes -- health, growth or organization.
A decrease in entropy is sometimes called syntropy.
Here is the Second Law of Thermodynamics -- (?)
| In a closed system entropy increases until it reaches a maximum value |
| Decreasing the entropy of an open system will be offset by an even greater increase in the entropy of its environment. |
A simple chemical reaction that combines hydrogen and oxygen provides a startling example of this principle --
| 2H2 + O2 ——–> 2H2O (steam) |
The system of uncombined
molecules on the left loses 11 units of entropy when it changes to
the more organized state on the right. However, the cost to the environment
is a gain of 150 entropy units! In a sense, the reaction taxed
its environment by a factor of almost 15 to improve its status.
Now
think of two insulated containers of water, each weighing ten pounds.
One is at 100°F, the other at 200°F. The air temperature
is 50°F. The separating insulation is
| Figure 7-6 Change and the unavailability of energy |
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removed, and the lukewarm
water mixes with the hot water. The mixture averages out to a temperature
of 150°F. This is closed system so the internal energy does
not change. But the mixed system has 35 BTU’s less available
energy so its entropy is higher.
The First Law requires
a balance. From the viewpoint of games, it is zero sum or
fair game. The Second Law requires an imbalance. It is a negative
sum or unfair game. These are not social or or political games,
where votes can change the rules. Nature makes these rules.
Ancient cultures recognized the Second Law and have provided us
with metaphorical guidelines ( = qualitative principles!) for avoiding
the increase of entropy --
· Waste
not, want not
· A stitch
in time saves nine
· An
ounce of prevention is worth a pound of cure
Exercise 7.13 Think of
three situations in your experience in which an incident caused
a considerable increase in entropy. Is it apparent that the energy
of prevention would have been much less than the energy of a cure
. . . ?
Exercise 7.14 ( Stephanie
)
6. Efficiency The (thermodynamic) efficiency
of a process is inversely related to the entropy. This is the ratio
of useful output to input and so is always less than 100%. There
is no internal storage, so the sum of the inputs must equal the
outgoing energy. The efficiency for the below process is 22.5%
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| Figure 7-7 Calculating efficiency | ||
Industrial
economies are built on heat engines, and much effort goes into improving
their efficiencies. The Big Three of heat engines are the Diesel
(oil), Otto (gasoline), and Rankine (steam) engines. Mileage
is a good, practical measure of the efficiency of engines used for
transportation. The increase in miles per gallon (mpg) for gasoline
engines has been significant over the past ten years. Sometimes
it is charged that oil companies repress engine designs that will
get 300+ mpg. The charges are based on calculations that convert
almost all the energy of gasoline into useful work. Unfortunately,
“the iron law of entropy” will exact its tax by sucking much of
the energy into the heat sink. Can engineers improve the design
of a gasoline engine so that it is almost 100% efficient . . . ?
The answer, unfortunately, is No. The thermodynamic
efficiency of internal combustion engines is 50-55%, and this is
a maximum. Actual efficiency is always less, running about
35% for current automobile engines.
Exercise 7.15 Find the
efficiency of each of the following --
 |
7. Kinetic and Potential Energy Physicists divide
energy into two classes, kinetic or moving energy, and potential or
stored energy. The kinetic energy (KE) of an object or system is the
energy it has by virtue of its motion. The potential energy (PE) of
an object or system is the energy possessed by virtue of its position
or structure. For example --
· A
stretched bow, upon release, transforms its PE to the KE of the arrow
in flight
· Water
as a cloud possesses gravitational PE; water in the form of falling
rain possesses KE
· The
PE in glucose ( a sugar) can be transformed into the KE of muscular
action
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| Figure
7-8 Potential energy (top) being tranformed to kinetic energy |
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Kinetic energy
is always given by the expression KE = mv2/2
, where m is the mass of the object or system, and v is its velocity.
This formula tells us that a car traveling at 60 mph has four times
the energy it would have at 30 mph, and at 90 mph, this jumps to
nine times the energy. So beware of speed. The square
on the velocity tem warns us of trouble, but it is easy to be misled
by the mass term. For example, a meteor two miles across traveling
at the same velocity as a meteor that is one mile across will do
much more damage on impact -- 800% more. ( Mass is proportional
to volume, and volume scales as the cube of a linear measurement.)
Kinetic energy is a measure of the rending or tearing action
in a collision.
Exercise 7.16 Who
has more KE, a 270 lb lioness charging at 60 fkt/sec or a 120 lb
cheetah charging at 90 ft/sec?
8.
More on Energy and Power
Forms of Energy
Energy can manifest itself in many forms.
It was different in each of the above three examples. The taut bow stores mechanical
energy, the cloud stores gravitational energy, and glucose stores chemical energy.
Other forms of energy are electrical, geological and thermal.
Some Units of Energy
| BTU | British Thermal Unit -- One BTU can raise the temperature of one pound of water one degree Fahrenheit (°F) | |
| Cal | Large or kilogram calorie -- One Cal can raise the temperature of one kilogram of water one degree Celsius (°C) | |
| cal | small or gram calorie -- One cal can raise one gram of water one degree Celsius | |
| ft-lb | The energy exerted by a force of one pound moving one foot | |
| KW-hr | The energy it takes to run a 1000 watt appliance or light for one hour | |
| joule | The energy exerted by a force of one newton moving one meter |
A Potpourri of Energy Relations
| One potato has about 100 food Cal. |
| One pound of coal generates about 13,000 BTU. |
| One barrel of oil generates about 160,000 Cal. |
| A burning tire generates the same heat as 2.5 gal of oil. |
Exercise
7.17
a) Which is larger, one BTU or one
Cal?
b) If all of the energy in 10 lbs of coal
went into heating a full 40 gal hot water tank, how much would it raise the
temperature of the water?
c) How
would you modify your answer to b in an actual situation where coal is being
burned to heat the water?
d) Estimate how much one Cal would raise
your body temperature
e) If all of the energy in the
potato you just ate went into raising your body temperature, what would happen
... ?
A Potpourri of Power Relations
| A small kerosene heater supplies about 10,000 BTU/hr. |
| One square meter of earth averages 4000 solar Cal/day. |
| A horse can output a steady one-quarter HP |
| (HP = 550 ft-lb per sec = 1 Horsepower!) |
| Energy | Power ( = Energy Flow ) |
| Cal | Cal/sec, Cal/hr, . . . |
| BTU | BTU/sec, BTU/hr, . . . |
| ft-lb | ft-lb per sec |
| kilowatt-hr | kilowatt |
| joule | joule/sec = watt |
| HP-hr | HP |
Exercise 7.18 Consult the Conversion Table at the end of this chapter for help in answering this exercise.
a) Find the mechanical equivalent (ft-lb per sec) to the heat output of a small kerosene heater.
b) What is the HP equivalent to the average solar power that falls on a square meter of earth?
c) Find the wattage equivalent of a horse’s steady output.
9. The Maximum Power Principle H.T. Odum writes, "Systems prevail that maximize the flow of useful energy" [10, p.6]. He re-expresses this idea as, “Those systems that survive in competition are those that develop more energy inflow and use it to meet the needs of survival” [9, p.32]. This Maximum Power principle has been a source of contention -- many natural systems seem to minimize energy flow or minimize entropy. It turns out that systems that have a ready flow of "quality" energy do maximize power. For example, viruses in a host, weeds in a garden or human colonizers, all tend to maximize energy throughput. This is often done via self-organizing, or autocatalytic units.
| Figure 7-9 Autocatalytic unit |  |
|
The path parameters measure the following flows --
| d | Depreciation (corrosion, inflation, leaks, etc.) | |
| h | Heat loss due to the work of production | |
| p | Production | |
| f | Feedback | |
| k | Net production (k = p - f) |
Conversion Table for Energy Units
| BTU | Cal | ft-lb | joule | kw-hr | |
| BTU | 1 | 3.97 | 3420 | ||
| Cal | 0.252 | 1 | 860 | ||
| ft-lb | 778 | 1 | 0.737 | ||
| joule | 1055 | 4186 | 1.36 | 1 | 3.60·106 |
| kw-hr | 1 | ||||
| 1 lb coal | 13000 | ||||
| 1 brl oil | 6.35·108 | 1.60·106 | |||
| 1 lb TNT |
How would you go from joules to ft-lbs?
Start with the blue column and read down to
joule. Then go across the row until you hit the ft-lb
column. The entry 1.36 tells you that there 1.36 joules in a ft-lb,
or 1.36 joules/ft-lb. (So this tells you that a joule is smaller
than a ft-lb.)
What
does the entry 3.97 tell us . . . ?
It's in the BTU
row and the Calorie column so it means
there are 3.97 BTU in a Cal or 3.97 BTU/Cal. (This tells us that a BTU is
smaller than a Cal -- it takes almost four of the to make a Cal.
Exercise 7.19 Complete the upper
part of the Conversion Table for Energy Units on the following page.