AP Environmental Science
Summer Packet
(This packet includes selected articles and exercises that must be completed prior to the first
lecture period.)
Selected Readings:
1.
A Hands-On Approach to Understanding Topographic Maps and Their Construction
http://apcentral.collegeboard.com/apc/members/repository/ap04_env_sci_topomaps_35750.
pdf
2.
A Primer About Ecology: Background Information for Humboldt County’s Ecology Day
Program http://www.unce.unr.edu/publications/files/nr/2009/cm0903.pdf
3.
Foresters’ Primer in Nutrient Cycling
http://www.srs.fs.usda.gov/pubs/gtr/uncaptured/gtr_se037.pdf
4.
Global Nitrogen Cycling Out of Control
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1247398/pdf/ehp0112-a00556.pdf
5.
Nutrient Cycling in Pastures
http://www.plantsciences.ucdavis.edu/gmcourse/module_resources/module1/resources/nutri
entcycling.pdf
Selected Exercises:
1.
2.
An Energy Primer for the PA Environmental Science Student (Attached, pp 2-9)
AP Environmental Science Summer Math Packet (Attached, pp 10-13)
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An Energy Primer for the AP Environmental Science Student
Even for practicing scientists and engineers, energy concepts and terminology can sometimes be
confusing and ambiguous. Confusion arises because different disciplines often employ different
systems of measurement and use specialized vocabulary unique to a particular industry. The
situation can be especially troublesome for the introductory environmental science student who
may not have completed even a first course in physics. And the problem is not alleviated by the
typical environmental textbook where energy terms are introduced only in a piecemeal fashion as
needed in the context of a specific environmental topic. Thus, the introductory environmental
science student is often left with a fragmentary, confusing, and unsatisfactory introduction to
energy concepts and terminology. This is particularly worrisome because energy use is at the
heart of most environmental problems. Moreover, the environmentalist must be able to
communicate with people in many different disciplines. Accordingly, he or she must be familiar
with the different systems of measurement and be able to convert readily from one to another.
This article provides a brief introduction to the major systems of measurement used in science
and technology with a special focus on energy terms useful for the environmentalist.
Systems of Measurement
There are two systems of measurement in common use in the world: the United States
Customary System (USCS, formerly called the British system) of feet, pounds, and seconds, in
everyday use in the United States, and the metric system of meters, kilograms, and seconds, in
use everywhere else. In 1960 the metric system was adopted by an international committee in
Paris as the worldwide standard for science and is now referred to as the Système International or
SI. The U.S. is the only major country that still uses the British system of measurement (even
Britain has gone metric!), but this system is well ingrained in American society and is unlikely to
see an early demise. A subset of the metric system is the centimeter-gram-second (cgs) system
that is commonly used in atomic physics and chemistry.
All physical quantities, such as velocity, acceleration, force, momentum, and energy, ultimately
can be expressed in terms of three basic units of length, mass, and time. These three quantities
are referred to as fundamental units because they can be used to define all other elements in a
particular system of measurement. The table below summarizes the fundamental units for the
three common systems of measurement.
System
Length
Mass
SI (mks)
meter
kilogram second
SI (cgs)
centimeter gram
USCS (fps) foot
slug
Time
second
second
Because the mass unit slug is uncommon, the USCS is referred to as the foot-pound-second (fps)
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system, but strictly speaking, the pound (lb) is a unit of force, not mass. Conversely, in the SI
system the mass unit of kilogram is often used to express force (of gravity), as in a person's
weight, for example. In this sense, a convenient conversion factor between the systems is to use
the "weight equivalent" of 2.2 lbs for a 1 kg mass.
Work and Energy
Physicists define energy as "the ability to do work," but in a sense this begs the question because
work itself is still undetermined. The term "work" in physics is defined as force multiplied by the
distance through which the force acts. Thus we get the idea that energy is the property that
allows one to move objects from one place to another and thereby accomplish some physical
labor or "work." Energy itself may appear in a variety of forms -- e.g., solar energy, electrical
energy, chemical energy, thermal energy, and nuclear energy -- but the bottom line is that all
forms can be used to do work. Thus, all units of energy must ultimately be reducible to those of
work -- i.e., force x distance. From Newton's law, we know that force is mass x acceleration. So
extending the above table, we have:
System
Force = Mass x Acceleration
SI (mks)
Newton kg
m/s2
SI (cgs)
dyne
gram
cm/s2
slug
ft/s2
USCS (fps) lb
And finally, we have the table for energy:
System
Energy = Force x Distance
SI (mks)
joule
newton meter
SI (cgs)
erg
dyne
cm
USCS (fps)
ft-lb
lb
ft
Note that although the newton and joule are named for persons, they are not capitalized when
used as a unit of measurement. However, the corresponding symbols (N and J) are capitalized
when used independently.
The Newton
The SI unit of force, the newton (N), is of course named in honor of Isaac Newton. From the
above, we see that 1 N = 1 kg-m/s2, which is equivalent to about 0.225 lbs. Note that 1 N is not
equal to the weight of 1 kg.
The Joule
Similar to the unit of force, the joule (J) is named in honor of Sir James Prescott Joule, a famous
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nineteenth-century British scientist who performed many precise energy experiments. One joule
is the amount of work done by a force of one newton acting through a distance of one meter.
From a practical, everyday standpoint, the joule is a relatively small amount of energy, but it is
used most often in scientific work. The energy content of one large donut, for instance, is about
106 joules.
The Calorie
Through a series of cleverly designed experiments with pulleys, weights, paddle wheels, and
precisely measured temperatures in containers of water, Joule convincingly demonstrated the
equivalence between mechanical energy and heat. Until that time, people thought that heat was
some sort of ephemeral property of materials, like a fluid, that was released when solid objects
were broken into smaller pieces. They called this property caloric, from which the term calorie
is derived. Joule showed that heat and mechanical energy are equivalent, and his careful
measurements gave us what we refer to today as the "mechanical equivalent of heat":
1 calorie = 4.186 joules.
You may recall that one calorie is the amount of heat required to raise the temperature of one
gram of water by one Celsius degree. One kilocalorie would increase the temperature of 1 kg of
water by the same amount. The kilocalorie is sometimes referred to as a "big" calorie and written
with a capital C, namely, as Calorie. Obviously, this practice has much potential for confusion,
so the reader must be constantly alert as to a writer's intention when speaking of calories. To
further confuse the issue, food calories are always "big" calories. Thus, when one speaks of 100
Calories in a slice of bread, for instance, the implication is that 100 kilocalories or 4.186 x 105 J
would be released through burning the dried biomass.
The energy content in fuels is measured by burning them to exhaustion and capturing the heat
that is released. This heat can be transferred, say, to a container of water where a temperature
increase is measured. Knowing that one calorie per gram is required to increase the temperature
of the water then allows one to determine the energy content of the fuel in terms of calories. This
number can then be converted to other energy units using Joule's conversion factor.
The Btu
Another popular unit of heat energy is the Btu (British thermal unit). One Btu is the amount of
heat required to raise the temperature of one pound of water by one degree Fahrenheit. Using the
conversion factors of 2.2 lbs/kg and 1.8 F°/C°, and Joule's equivalent, we find that:
1 Btu = 252 cal = 1055 J.
One Btu is approximately the amount of heat released by burning one large kitchen match.
Btus are commonly used in the United States to rate water heaters, furnaces, and air conditioners.
A typical natural gas household water heater, for instance, might be rated at 40,000 Btu/h and a
furnace at twice this, or 80,000 Btu/h. These numbers, of course, give the rate at which heat can
be produced by the burners of these units. The heating values for fuels are often stated in terms
of Btus per unit weight. Coal, for instance, has a typical heating value of 25 million Btu/ton, and
petroleum 37 million Btu/ton.
The Therm
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Gas companies in the U.S. often measure sales in terms of "thermal units" or therms. One therm
is defined as 100,000 Btu, and natural gas at normal temperature and pressure has a heat value of
1,030 Btu/ft3. Thus, one therm is very nearly equal to 100 cubic feet of natural gas:
1 therm = 105 Btu / 1,030 Btu/ft3 = 97.1 ft3 ≈ 100 ft3.
Gas companies also use "American Engineering" terminology instead of standard SI scientific
notation. In this notation, the Latin abbreviations of C for 100 and M for 1000 are employed as
numerical prefixes, but because of the potential confusion between the standard scientific
notation of C for centi (10-2) and M for mega (106), the engineering abbreviations are not usually
written with capitalization. For instance, 1 ccf = 100 cubic feet, and 1 mcf = 1,000 cubic feet,
and one million cubic feet is written as 1,000 x 1,000 cf or 1 mmcf.
Power
Power is the term that is used to describe energy flow. Power is defined as "the time rate of
doing work" and normally is measured in joules/second. In the SI system, the unit of power is the
watt (W), named in honor of James Watt, inventor of the steam engine. 1 watt = 1 joule/second.
No separate unit is ascribed to power in the cgs system. In the USCS system, power is measured
in "practical" units of horsepower (hp), where 1 hp = 550 ft-lbs/s. This is equivalent to 746 watts,
or about 0.75 kW.
Perhaps because most electric appliances are rated in terms of their power requirements, power
and energy are often confused when dealing with electrical energy. But just as when filling the
tank of your car at the gas station you must ultimately pay for the total number of gallons
pumped, not the rate at which you pumped it, so with electricity we pay for the total number of
joules of electrical energy consumed, not the power or rate at which it was delivered.
In the U.S., electrical energy is usually measured in terms of kilowatt-hours (kWh), because this
is a practical unit for the utility company as well as the customer. The relation between kilowatthours and joules is easy to determine:
1 kWh = 1,000 J/s x 3,600 s = 3.6 x 106 J.
Again, we see how small a joule is in practical terms. One kWh is the energy required to power
ten 100-watt lightbulbs for one hour. The average home in the U.S. uses about 10,000 kWh of
electrical energy per year.
Electric Power Plants
Electric utility power plants are rated in terms of their capacity to deliver electric power. For
instance, a large coal-fired or nuclear plant might be rated at 1,000 MWe (megawatts). The "e"
subscript on the W stands for "electric" and is a signal that the rating is for the "output" capacity
of the plant, not the energy input. Input energy is usually measured in terms of the heating value
for the fuel -- Btus for coal, for instance. If the plant operates at, say, 40 percent efficiency, then
the energy input required for such a plant can be computed as follows:
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If this energy is supplied by coal with a heating value of 25 x 106 Btu/ton, then coal would need
to be input at a rate of
Operating at full capacity 24 hours a day, such a plant would consume about three million tons of
coal per year.
Solar Energy
Another valuable use of power in environmental analyses deals with solar energy. The sun, of
course, provides radiant energy for all life on earth, and the rate at which this energy is received
is referred to as solar flux, representing the power per unit area received at a given location. At
the position of the Earth's orbit, this number is about 1,400 W/m2 and is referred to as the solar
constant. This means that a flat panel of 1 m2 placed outside the Earth's atmosphere and oriented
perpendicular to the sun's rays would receive 1,400 joules per second of solar energy.
The atmosphere absorbs about half of this energy, so that 700 W/m2 is about the maximum
amount that reaches the Earth on a hot summer day in the tropics. Averaging over day and night
for all seasons and all latitudes, this is further reduced to about 240 W/m2 as the average solar
radiation received at the Earth's surface. Cloud cover and other factors reduce these numbers
even further. In the U.S., for example, Tucson, Arizona, enjoys an annual average solar flux of
250 W/m2, but Cleveland receives only 160 W/m2. Obviously, such numbers have implications
for the merits of solar heating and cooling as well as biomass growth in various locales.
Summary
Because energy plays a fundamental role in all environmental problems, it behooves the student
to become familiar at an early stage with energy concepts and terminology. The environmental
scientist must also get accustomed to specialized terms that are used in different disciplines and
industries. The gas company is not going to convert cubic feet into Btus for you, just as the
electric company is not going to convert kWh to joules. It is the responsibility of the
environmental student to be able to put units on a common basis in order to make valid
comparisons. For instance, is a natural gas furnace more economical or more environmentally
benign than baseboard electric heating for an average home? Could solar energy supply all the
heating needs for a home in Cleveland? How much electricity could be generated by installing
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solar panels on the roof of a home in Arizona? How much biomass can be grown on an acre of
land in Missouri? A thorough understanding of energy units and terminology will go a long way
to help the environmentalist make such analyses easy and commonplace.
Practice Questions
1. Given that 1 kcal of heat is required to increase the temperature of 1 kg of water by 1°C:
a. How many kcals would be required to heat 100 kg of water by 20°C for a bath?
b. How many joules is this?
c. How many Btus?
d. If your water heater can supply 40 kBtu/h, how long will it take to heat this water?
2. a. Given that 1 kWh = 3.6 MJ and that 1 Btu = 1055 J, show that 1 kWh = 3412 Btu.
b. Why would it be incorrect to use this conversion factor directly to determine the amount of
coal required to generate electricity in a power plant?
3. A typical home in the northern U.S. might require 120 MBtu of heat for the average winter.
a. If this heat were supplied by a natural gas furnace operating at 60 percent efficiency, how
many cubic feet of gas would need to be purchased?
b. At a cost of $0.90/ccf, what would it cost to heat this house for one season?
c. If a new 80 percent efficient furnace could be installed at a cost of $4,000, how long would it
take to pay back the cost of this furnace assuming gas prices remained the same?
4. Suppose the house in question 3 is located in Cleveland where the annual average solar flux is
160 W/m22. If 10 m2 of solar panels operating at 20 percent efficiency were installed on this
house to collect and store solar energy in the form of hot water:
a. How much energy could be gained in one year in this manner?
b. What fraction of the annual heating requirement is this?
c. Using the hot-water heating requirements for a bath from question 1(c), how many hot baths
would this energy supply in one year?
5. The annual average solar flux in Tucson is 250 W/m2. Suppose 10 m2 of solar electric panels
operating at 10 percent efficiency were installed on a home there.
a. How many kWh of electricity could be collected by these panels in one year?
b. What fraction of the annual electrical requirement of 10,000 kWh for the average home does
this represent?
c. How many square meters of solar panels would be required to supply 10,000 kWh per year?
6. Solar energy is converted naturally into wood biomass with an efficiency of about 0.1 percent.
Suppose a wood lot of 100 hectares (106 m2) is located in Missouri, where the average annual
solar flux is 200 watts/m2. Given that the heat value for wood is 12 MBtu/ton, how many tons of
wood can be produced by this property each year?
7. With moderate winds, a modern large wind turbine can generate about 250 kW of electricity,
whereas a large nuclear power plant can generate 1,000 MW.
a. How many wind turbines would be required to give the same output as one nuclear power
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plant?
b. Discuss some of the advantages and disadvantages to providing electrical power by each
method.
8. Batteries are usually rated in terms of ampere-hours, indicating the current that the cell is
capable of delivering for a specified time. A typical D-cell flashlight battery, for instance, might
be rated at 3 ampere-hours. The total electrical energy available from such a battery is found by
multiplying the ampere-hour rating by the battery voltage. Thus this same 1.5 volt D cell could
deliver 4.5 watt-hours of electrical energy.
Convert this energy to kWh and compare the cost of electrical energy derived in this manner to
that of standard "grid-based" electricity. Assume that the battery costs $1.00 and that electricity
from the power company is available at $0.10/kWh.
9. The table below gives prices and heat energy content for various fuels that are commonly used
for home heating. Fuel prices are given as a per-unit cost for fuel delivered to the home.
Complete the table by filling in the last two columns and thereby compare the cost of home
heating by these various methods. In your computations, assume that the home requires 120
MBtu of heat for a season and that gas- or oil-fired furnaces operate at 80 percent efficiency.
Assume that electrical heating is 100 percent efficient.
Fuel
Price
Energy Content of
Fuel
Nat. gas
$1.14/ccf
1030 Btu/cf
Propane
$1.69/gal
92 k Btu/gal
Fuel oil
$1.93/gal
133 k Btu/gal
Cost per
MBtu
Cost of Home
Heating
Electricity $0.10/kWh 3412 Btu/kWh
Thomas B. Cobb is professor emeritus of physics and former director of environmental programs
at Bowling Green State University in Ohio. Dr. Cobb is a former member and chair of the APES
development committee, and has participated in readings for six of the seven years that the
national exam has been given. At BGSU he introduced a course in environmental physics that is
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taken by most environmental majors and is active in presenting training workshops in
environmental science for the College Board.
Page 9 of 13
AP Environmental Science Summer Math Packet
1.
Express the following quantities in scientific notation:
a.158 000 km
f.
0.000 000 006 13 m
b.0.000 009 782 L
g.
12 552 000 J
c.837 100 000 cm3
h.
0.000 008 004 g/L
d.6 500 000 000 mm2
i.
0.010 995 kg
e.0.005 93 g
j.
1 050 000 000 Hz
2.
Perform the following calculations, and express the result in scientific notation with the
correct number of significant figures:
a.2.48 102 kg + 9.17 103 kg + 7.2 101 kg
b.4.07 10 5 mg + 3.966 10 4 mg + 7.1 10 2 mg
c.1.39 104 m3 + 6.52 102 m3 4.8 103 m3
d.7.70 10 9 m 3.95 10 8 m + 1.88 10 7 m
e.1.111 105 J + 5.82 104 J + 3.01 106 J
f.9.81 1027 molecules + 3.18 1025 molecules 2.09 1026 molecules
g.1.36 107 cm + 3.456 106 cm 1.01 107 cm + 5.122 105 cm
3.
Perform the following computations, and express the result in scientific notation with the
correct number of significant figures:
a.1.54 10 1 L 2.36 10 4 s
b.3.890 104 mm 4.71 102 mm2
c.9.571 103 kg 3.82 10 1 m2
d.8.33 103 km 1.97 102 s
e.9.36 102 m 3.82 103 m 9.01 10 1 m
f.6.377 104 J 7.35 10 3 s
4.
Your electric company charges you for the electric energy you use, measured in kilowatthours (kWh). One kWh is equivalent to 3 600 000 J. Express this quantity in scientific notation.
5.
The pressure in the deepest part of the ocean is 11 200 000 Pa. Express this pressure in
scientific notation.
6.
Convert 1.5 km to millimeters, and express the result in scientific notation.
7.
Light travels at a speed of about 300 000 km/s.
a.Express this value in scientific notation.
b.Convert this value to meters per hour.
c.What distance in centimeters does light travel in 1 s?
8.
There are 7.11 1024 molecules in 100.0 cm3 of a certain substance.
a.What is the number of molecules in 1.09 cm3 of the substance?
b.What would be the number of molecules in 2.24 104 cm3 of the substance?
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c.What number of molecules are in 9.01
10 6 cm3 of the substance?
9.
The number of transistors on a particular integrated circuit is 3 578 000, and the
integrated circuit measures 9.5 mm 8.2 mm.
a.What is the area occupied by each transistor?
b.Using your answer from (a), how many transistors could be formed on a silicon sheet that
measures 353 mm 265 mm?
10.
A solution has 0.0501 g of a substance in 1.00 L. Express this concentration in grams per
microliter.
11.
Cesium atoms are the largest of the naturally occurring elements. They have a diameter
of 5.30 10 10 m. Calculate the number of cesium atoms that would have to be lined up to give a
row of cesium atoms 2.54 cm (1 in.) long.
12.
The neutron has a volume of approximately 1.4 10 44 m3 and a mass of
1.675 10 24 g. Calculate the density of the neutron in g/m3. What is the mass of 1.0 cm3 of
neutrons in kilograms?
13.
The pits in a compact disc are some of the smallest things ever mass-produced
mechanically by humans. These pits represent the 1s and 0s of digital information on a compact
disc. These pits are only 1.6 10 8 m deep (1/4 the wavelength of red laser light). How many of
these pits would have to be stacked on top of each other to make a hole 0.305 m deep?
14.
22 400 mL of oxygen gas contains 6.022 1023 oxygen molecules at 0 C and standard
atmospheric pressure.
a.How many oxygen molecules are in 0.100 mL of gas?
b.How many oxygen molecules are in 1.00 L of gas?
c.What is the average space in milliters occupied by one oxygen molecule?
15.
The mass of the atmosphere is calculated to be 5.136 1018 kg, and there are
6 500 000 000 people living on Earth. Calculate the following values.
a.The mass of atmosphere in kilograms per person.
b.The mass of atmosphere in metric tons per person.
c.If the number of people increases to 9 500 000 000, what is the mass in kilograms per person?
16.
The mass of the sun is 1.989 1030 kg, and the mass of Earth is 5.974
How many Earths would be needed to equal the mass of the sun?
1024 kilograms.
17.
A new landfill has dimensions of 2.3 km 1.4 km 0.15 km.
a.What is the volume in cubic kilometer?
b.What is the volume in cubic meters?
c.If 250 000 000 objects averaging 0.060 m3 each are placed into the landfill each year, how
many years will it take to fill the landfill?
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18.
A dietary calorie (C) is exactly equal to 1000 cal. If your daily intake of food gives you
2400 C, what is your intake in joules per day? (1 cal = 4.184 J)
19.
Determine the number of significant figures in the following measurements:
a.0.0120 m
f.
1000 kg
b.100.5 mL
g.
180. mm
c.101 g
h.
0.4936 L
d.350 cm2
i.
0.020 700 s
e.0.97 km
20. Round the following quantities to the specified number of significant figures:
a.5 487 129 m to three significant figures
b.0.013 479 265 mL to six significant figures
c.31 947.972 cm2 to four significant figures
d.192.6739 m2 to five significant figures
e.786.9164 cm to two significant figures
f.389 277 600 J to six significant figures
g.225 834.762 cm3 to seven significant figures
21. Perform the following calculations, and express the answer in the correct units and number of
significant figures.
a.651 cm 75 cm
d. 360 cm 51 cm 9.07 cm
b.7.835 kg 2.5 L
e. 5.18 m 0.77 m 10.22 m
c.14.75 L 1.20 s
f. 34.95 g. 11.169 cm3
22.
Perform the following calculations, and express the answer in the correct units
and number of significant figures.
a.7.945 J + 82.3 J 0.02 J
b.0.0012 m 0.000 45 m 0.000 11 m
c.500 g + 432 g + 2 g
d.31.2 kPa + 0.0035 kPa 0.147 kPa
e.312 dL 31.2 dL 3.12 dL
f.1701 kg + 50 kg + 43 kg
23. A rectangle measures 87.59 cm by 35.1 mm. Express its area with the proper number of
significant figures in the specified unit:
a.in cm2
b.in mm2
c.in m2
24. A box measures 900. mm by 31.5 mm by 6.3 cm. State its volume with the proper number of
significant figures in the specified unit:
a.in cm3
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b.in m3
c.in mm3
25. A 125 mL sample of liquid has a mass of 0.16 kg. What is the density of the liquid in the
following measurements?
a.kg/m3
b.g/mL
c.kg/dm3
26. Perform the following calculations, and express the results in the correct units and with the
proper number of significant figures.
a.13.75 mm 10.1 mm 0.91 mm
b.89.4 cm2 4.8 cm
c.14.9 m3 3.0 m2
d.6.975 m 30 m 21.5 m
27. What is the volume of a region of space that measures 752 m 319 m 110 m? Give your answer in
the correct unit and with the proper number of significant figures.
28. Perform the following calculations, and express the results in the correct units and with the
proper number of significant figures.
a.7.382 g + 1.21 g + 4.7923 g
b.51.3 mg + 83 mg 34.2 mg
c.0.007 L 0.0037 L + 0.012 L
d.253.05 cm2 + 33.9 cm2 + 28 cm2
e.14.77 kg + 0.086 kg 0.391 kg
f.319 mL + 13.75 mL + 20. mL
29. A container measures 30.5 mm 202 mm 153 mm. When it is full of a liquid, it has a mass
of 1.33 kg. When it is empty, it has a mass of 0.30 kg. What is the density of the liquid in
kilograms per liter?
30. If 7.76 km of wire has a mass of 3.3 kg, what is the mass of the wire in g/m? What length in
meters would have a mass of 1.0 g?
31. A container of plant food recommends an application rate of 52 kg/ha. If the container holds
10 kg of plant food, how many square meters will it cover
(1 ha = 10 000 m2)?
32. A chemical process produces 974 550 kJ of energy as heat in 37.0 min. What is the rate in
kilojoules per minute? What is the rate in kilojoules per second?
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