Warm Up #1
• What are some various forms of energy (what
do we use to power stuff)?
• Of the ones you listed in #1, which ones are
better? Why are they better?
• What is horsepower?
Warm Up #2
• Where have you seen the word “watts” being
used before? What do you think it means?
• How can you tell a car, like a Acura NSX, is
powerful? (i.e. what quality about the car
makes it powerful?)
• How many meters are in a kilometer? What
about a megameter (yes, that’s a real thing)?
Energy: Renewable and NonRenewable
Energy Math
Part I
Laws of Energy (Thermodynamics)
• Law 1: Energy cannot be created or destroyed
– You can’t make something out of nothing
• Law 2: When energy is converted from one
form to another, some of that energy is lost
– Moving up food chain, some energy lost as HEAT
Other Forms of Energy: Part 1
• Horsepower (HP) - measures the power
generated by horses (original definition)
– Ex. 1 horsepower = power of 1 horse
• 1 HP = 746 watts
– Random, I know. Sorry about it.
• Ferrari vs. Prius
Other Forms of Energy: Part 2
• British Thermal Units (Btu) – Amount of
energy needed to raise 1 lb. of water by 1oF
– Think of it like a calorie (food)
Random Conversions:
• 1 watt = 3.4 Btu
• 1 HP = 2,540 Btu
Measuring Energy: Watts
• Watt – standard unit of measurement for
• Two forms you will see:
• Kilowatts (1 kW = 1000 watts)
– 1x103 watts
• Megawatts (1 MW = 1,000,000 watts)
– 1x106 watts
Kilowatt Hours & Your Electric Bill
• Your electric bill – measures amount of power used
over a period of time
• You will see: Kilowatt Hours (kWh) – amount of watts
generated in 1 hour
– Kilowatts x hours = kWh
For these conversions:
• Know what you are starting with
• Know what they are asking for
• Convert accordingly
Warm Up #6
A resident of Beverly Hills, a community of 10,000
homes, uses on average about 5,000 kilowatt hours
of electricity per year. The cost of electricity in this
community is $0.20 per kWh.
• How much electricity would a resident use in a 20
year period?
• How many kWh of electricity does all of Beverly
Hills use in one year?
• What would their electric bill be as a community for
twenty years?
Warm Up #7
The Cobb family’s current electric hot-water heater requires
0.20kWh/gallon of energy, costing $0.10/kWh. Each person in
the family of four showers once a day, 10 min. each. Each
shower is approx. 5.0 gallons per min. Calculate:
• Total amount of water the family uses per year taking showers.
• The annual cost of electricity for family showers, assuming 2.5
gallons per min. of water is used from the water heater.
• The family wants to replace their hot-water heater with a new,
$1,000 more efficient model. It requires only 0.10 kWh/gallon
of energy. How many days would it take to recover the initial
• Describe two practical measures the family could take to
reduce overall water use.
• Describe two practical measures that the Cobb family can
lower their overall energy consumption (other than hot water).
Practice Problem
West Fremont is a community of 3,000 homes. A
small coal-burning plant supplies the electricity of
the town, with a capacity of 12 megawatts (MW).
The average household consumes 8,000 kWh of
electrical energy every year, at a cost of $0.10 per
kWh. The town leaders suggest switching to wind
power. They want to install 10 wind turbines, each
with a 1.2 MW capacity, and each costing $3
million. Their lifespan is 25 years.
Practice Problem Questions
(a) Assuming the power plant is operating at full capacity
for 8,000 hours/yr. How many kWh of electricity can
be produced by the plant each year?
(b) At the current rate of energy per household, how
many kWh of electrical energy does the community
consume in 1 year?
(c) Compare your answers of (a) and (b) and explain why
you would not expect their answers to match.
(d) Assuming the energy needs do not change during the
25-year lifespan of the wind turbines, what would the
cost of electricity be over 25 years (in $/kWh)?
(e) Identify and explain TWO environmental benefits of
switching to wind power, and TWO environmental
costs for switching to wind power from coal.
Warm Up # 3
A wind turbine in Palm Springs, a community with
800 turbines, uses on average about 10,000
kilowatt hours of electricity per year. The cost of
electricity in this community is $0.20 per kWh.
• Calculate the amount of energy generated from 1
turbine in 15 years.
• Calculate the amount of energy generated by all
of the wind turbines in 1 day
• For this day, how much would it cost the people
of Palm Springs
Practice Problem
For a certain dairy farm with 500 cows, the cost of installing a
digester is approximately $400,000. Assume that the farm uses
800,000 kilowatt-hours (kWh) of electricity each year at a cost of
$0.10 per kWh. The waste from a single cow can produce 3.0
kWh of electricity each day.
(c) Assuming that the cost of electricity remains constant and the
farmer starts using the manure from the cows in an anaerobic
digester to produce electricity on the farm, calculate:
• (i) The number of kWh of electricity that can be produced in one
• (ii) The amount of money the farmer can save in one year, NOT
counting the installation cost of the digester. (You may round your
answer to the nearest $1,000.)
• (iii) The amount of time, in years, that it will take to recover the
cost of installing an anaerobic digester on the farm. (You may
round your answer to the nearest whole number of years.)
(d) Calculate the minimum number of cows the farm would need to
produce 800,000 kWh of electricity per year.
Warm Up #4
You live in a community of 3,000 homes that rely on coal as a source of fuel.
The average home uses 8,000 kwh of energy per year at the cost of
Instead, town members want to switch to wind power; installing 10 wind
turbines ($3 million each) which will last 25 years.
• List two pros and two cons for switching to wind power.
• How much energy does your entire community use per year?
• If the energy needs stay the same over the 25 year lifetime of
the wind turbines, what would be the cost for the community
for wind power (in $/kwh)? How does it compare to the cost
of coal?
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