1. A person in the US uses an average of 300 Gigajoules of primary energy per year. On a continuous basis, day and night, how many kilowatts of primary energy does the person use?

The following list gives the energy content of some primary energy sources:

Coal 28 GJ/tonne
Natural gas 1 GJ/1000 cubic feet
Biomass 18 GJ/ dry tonne; one hectare of land produces 15 dry tonnes
Oil 6 GJ per barrel (42 gallons per barrel)
Solar energy maximum = 1 kW/m2; US average = 200 watts/m2
Also, for gasoline 1 gallon = 0.12 GJ

These sources can be converted to electricity, heat and transportation fuels with the following energy conversion efficiencies.

Coal can be converted to electricity at 40% efficiency
Biomass can be converted to electricity at 40% efficiency
Natural gas can be converted to electricity at 50% efficiency, and heat at 80% efficiency.
Oil can be converted to gasoline at 90% efficiency
Solar energy can be converted to electricity at 12% efficiency.
Biomass can be used to make liquid transportation fuels at 60% efficiency.

A person uses 300 gallons of gasoline, and 10,000 kWh of electricity per year.

How much coal, natural gas or biomass would be needed each year to make electricity for this person? For biomass or solar how much land would be needed?

How many barrels of oil would be used per year to make gasoline? If biofuels were used instead, how much land would be required to grow the biomass?

2. An engine operates at 1000 degrees C and rejects heat to the environment at 50 degrees C. The company brochure claims that the engine is 80% efficient at producing mechanical work from heat. Is this a reasonable claim? Why or why not?

3. Calculate the present value of the following expenses, assuming a discount rate of 8%.

a) $100 spent 10 years from now

b) $30 spent 2 years from now

c) a sum of expenses:

$100 in year 1
$300 in year 2
$200 in year 3
$150 in year 4
$50 in year 5

4. If you have $1000 now, and invest it at 10% rate of return, how much will it be worth in 10 years, in 30 years?

5. The "PowerGen" company is building an 100 Megawatt (1 MW =106 watt) natural gas-fueled electric power plant. PowerGen obtains a loan at 6% interest to finance building the plant over three years. PowerGen spends the following total amounts each year (for equipment, engineering, construction).

Year 1: $50 million
Year 2: $25 million
Year 3: $100 million

The plant starts producing electricity in year 4.

a) What is the present value in year 4 of the total capital investment in building the plant, counting interest during construction?

The power plant operates at an average annual capacity factor of 80%.

b) How many hours per year does the plant operate on average? How many kilowatt hours (kWh) of electricity are produced per year?

The energy conversion efficiency of natural gas to electricity in the plant is 40%. (40% of the energy in natural gas is converted to electricity). Natural gas costs $4 per Gigajoule (GJ). (1 GJ = 277.8 kWh)

c) How much natural gas is used per year to produce electricity?

d) What is the total cost each year for natural gas for the power plant?

The plant operates for 20 years after opening. PowerGen's investors expect a 12% rate of return on their investment.

e) What is the capital recovery factor CRF, assuming a plant lifetime of 20 years?

Fixed operation and maintenance costs for the plant (labor) are 3% of the total capital investment cost of the plant.

Find the present value of:

f) the total capital investment in building the plant

g) the natural gas input to the plant

h) the fixed operation and maintenance costs

i) Find the lifecycle cost of the plant ($)

j) What is the annualized lifecycle cost of the plant ($/yr)?

k) Estimate the levelized cost of electric power from this plant ($/kWh).

l) What is the levelized cost of electricity if the rate of return is 6%, 20%

6. A wind power turbine produces a maximum electrical output of 500 kilowatts. The turbine has a 15-year lifetime and the discount rate is 10%. The wind turbine costs $1 million for equipment prior to installation. Operation and maintenance costs are $50,000 per year. The capacity factor depends on where the turbine is installed. The power producer is considering two possible sites. A nearby site has a capacity factor of 30%, and construction and installation would add $100,000 to the cost. A more distant site with a more favorable wind resource has a capacity factor of 38%, but construction costs are $250,000. Which site is better, if the goal is produce the cheapest electricity?

A more expensive turbine would last for 20 years instead of 15 years and would give a capacity factors of 33% and 41% instead of 30% and 38%. The better turbine costs $1.5 million. Is it worth buying the more costly turbine?