Environmental Calculations - Rachel V Salyer's Blog



AP Environmental Calculations

Dimensional Analysis

• Show all your work on a separate sheet of paper; partial credit is given for partial solutions to problems. If the answer is not correct, you are not likely to receive credit for correct thinking if there is no evidence of this process on paper.

• All problems must be solved using dimensional analysis.

• Organize your answers as clearly and neatly as possible, showing the steps you took to reach your solution. If your reasoning can not be followed, you are less likely to receive credit for it.

• It is important to pay attention to units for quantities that have them. If you keep track of units as you do calculations, it can help you express your answers in terms of the proper units. It is possible to lose points if the units are wrong or are missing from the answer.

( 1 farmer requires 1 hen/day

( 1 hen eats 25 grasshoppers/day

( 1,000 grasshoppers have a mass of 1 kg

( 1 grasshopper requires 30 g of soy/yr

( 1 human requires 600 grasshoppers/day

( dry soybeans have about 3.3 cal/g

1. Calculate the number of grasshoppers a hen needs per year.

|1. | 1 hen |25 grasshoppers |365 days |= |9,125 grasshoppers |

| | |hen ? day |year | |year |

2. How many grasshoppers are needed for a year’s supply of hens for the farmer each year?

3. What is the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year?

4. How many kilograms of soybeans are needed to feed all the grasshoppers for one year?

5. Estimates of early Native American hunter-gather societies indicate that a person could collect about 90 kg (200 lbs) of grasshoppers per hour, when they are abundant. Now suppose the farmer chose to eat grasshoppers instead of hens. How many people could the grasshoppers feed, compared to the one person that the hen fed?

6. The farmer needs to consume 3,000 cal/day. If he ate only soybeans instead of the hens or the grasshoppers, how many people would his soybean crop feed (see your response to Question 4)?

1 kWh = 3.41 x 103 BTU ( British Thermal Units)

1 BTU = 1,055 J (joules)

1 pound of bituminous coal = 12,000 BTU

1 barrel of oil = 5.6 x 106 BTU

1 ft3 of natural gas = 1,030 BTU

1 g 235U = 4.0 x 107 BTU

1 tire = 250,000 BTU

7. The average American uses 10,000 kWh of energy. Convert kWh to cubic feet of natural gas.

8. How much coal would be burned to provide the energy?

9. How much uranium would be needed to provide the energy?

10. The cost for U3O8, the primary nuclear reactor fuel is $0.022 per gram. What would be the cost of the uranium to generate your electricity?

11. Coal costs about $24.38 per ton (2,000 pounds), and the cost of natural gas for electric utilities, on the average is about $4.67 per 1,000 cubic feet. Calculate the cost of these two fuels to produce electricity.

12. How many used car tires would be required to supply the electricity if the tires burn at 60% efficiency?

Coral reefs are produced when corals acquire calcium ions (Ca2+ ) and carbonate ions(CO32- ) from seawater and deposit solid CaCO3 to form their exoskeletons. Scientists are concerned that relatively rapid decreases in ocean water pH will hinder the deposition of CaCO3. Use the following assumptions below to perform the following calculations:

( Assume that the total global area of corals growing in reefs is 2.5 x 1011 m2.

( Assume that corals grow only vertically and that the average vertical growth rate of corals is 3 mm/year

( Assume that average density of CaCO3 in corals is 2 x 103 kg/m3

13. Calculate the current annual global increase in volume, in m3 of CaCO3 in coral reefs. Show all steps in your calculation.

14. Calculate the current annual global increase in kg of CaCO3 in coral reefs. Show all steps in your calculation.

15. Because of ocean acidification, it is expected that in 2050 the mass of CaCO3 deposited annually in coral reefs will be 20 percent less than is deposited currently. Calculate how much less CaCO3 in kg, is expected to be deposited in 2050 than would be deposited if ocean water pH were to remain at its current value.

A grid-connected residential PV system is placed on the roof of a 2,000-square-foot suburban house. The PV array with an area equal to 50 square meters covers half of the south-facing part of the roof. The power rating of this PV system is 5.0 kW, meaning that it will produce 5.0 kW under peak sunlight conditions. The installed cost of this system is $50,000.

16. The PV system is operating in a location where the annual average daily incident solar energy (the insolation) on the array equals 5.0 kWh/m2/day. Calculate the average amount of solar energy incident on the PV array each day in kWh/day.

17. The efficiency of the PV system equals 10 percent. Calculate the daily average electric energy produced by this system in kWh/day.

18. Over the next 20 years, United States annual electric energy consumption is projected to increase by 1.5 trillion kWh/year. How many rooftop PV systems would be needed to supply just 10 percent of this additional energy?

19. Assuming the electric energy produced by these PV systems is worth $0.10 per kWh, these residential systems would generate electric energy worth $15 billion/year. Calculate the simple payback period in years for these PV systems. (Payback period is the time it takes for a system’s net benefits to equal its cost)

Consider a wind turbine that is rated at 1.5 MW. This means that with sufficiently high winds, it will produce 1.5 MW or 1,5000 kW of power. The installed cost of this turbine is $1.5 million. A single turbine would produce enough energy for 1,000 homes for a year.

20. If this turbine runs at its rated power 100 percent of the time for a full year, how much energy would it produce in a year?

21. This wind turbine has a capacity factor equal to 0.38. This means that over a year, it will produce only 38 percent of its theoretical maximum energy production. How much energy does this turbine actually produce in a year (in million kWh/year)?

22. Calculate the cost of installing these wind turbines to meet the energy needs of an area with 1,000,000 homes.

23. Assuming the electric energy produced by these turbines is worth $0.05 cents per kWh, these turbines would generate electric energy worth $7.5 billion per year. Calculate the simple payback period for these turbines. (Payback period is the time it takes for a system’s net benefits to equal it cost.)

1 calorie = 4.186 joules

1 Btu = 252 cal

1 therm = 100 ft3

1 ft3 = 1000 Btu

1 kWh = 3.6 x 106 joules

24. 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. How many kcals would be required to heat 100 kg of water by 200 C for a bath?

25. How many joules is this?

26. How many Btus is this?

27. If your water heater can supply 40 kBtu/h, how long will it take to heat this water?

28. A typical Michigan home in the northern U.S. might require 120 Mbtu of heat for the average winter. How many cubic feet of natural gas would be needed to heat this home if the furnace operated at 60 percent?

29. At a cost of $0.90/ccf (100 ft3), what would it cost to heat this house for 1 year?

30. 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?

31. The annual average solar flux in Tucson, AZ is 250 W/m2. Suppose 10 m2 of solar electric panels operating at 10 percent efficiency were installed on a home in Tucson. How many kWh of electricity could be collected by these panels in one year?

32. What fraction of the annual electrical requirement of 10,000 kWh for the average home does this represent?

33. How many square meters of solar panels would be required to supply 10,000 kWh per year?

34. 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. How many wind turbines would be required to give the same output as one nuclear power plant?

Scientists say microalgae are the most efficient organisms at converting sunlight to energy. In fact, they beat other oil crops for production per acre. 70% of this oil can be recovered by pressing the algae; over 90% can be recovered by solvent extraction. The resulting oil can be used for heating, for electricity generation, or for making other fuels, like biodiesel.

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35. Calculate the number of acres required to produce 1,000 gallons of oil in one year from (a) microalgae and (b) soybeans.

The city of Fremont operates a municipal solid-waste landfill. As represented in the diagram below, the annual precipitation in Fremont is 200 mm/year: 50% of this water infiltrates through the landfill cover soil into the waste, and 50% drains off the landfill. A drainage system withdraws 90% of the leachate generated within the landfill for treatment. The rest of the leachate travels through the bottom liner of the landfill into the surrounding soil. Most of the cadmium disposed of in the landfill remains in the landfill; the leachate withdrawn from the landfill by the drainage system has an average cadmium concentration of 2.0 g/m3. Pumped to a treatment station, the leachate is treated at a cost of $10/m3.

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36. Calculate the volume, in m3 of each of the following: (a) The water infiltrated through the landfill per year (b) The leachate that is treated per year (c) The leachate that is not treated per year.

37. Given that the cadmium concentration in the water draining from the landfill is 2.0 g/m3, calculate the mass in kg of cadmium that is released into the surrounding soil per year.

38. What is the annual cost of treating the leachate from the drainage system?

The Cobb family of Fremont is looking at ways to decrease their home water and energy usage. Their current electric hot-water heater raises the water temperature to 1400 F, which requires 0.20 kWh/gallon at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute.

39. Calculate the total amount of water that the family uses per year for taking showers. Show all your work and include units with your answers.

40. Calculate the annual cost of the electricity for the family showers, assuming that 2.5 gallons per minute of the water used if from the hot-water heater. Show all your work and include units with your answers.

41. The family is considering replacing their current hot-water heater with a new energy efficient hot-water heater that costs $1,000 and uses half the energy that their current hot-water heater uses. How many days would it take for the new hot-water heater to recover the $1,000 initial cost?

Use the topographic map below to answer the following question.

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42. Calculate the slope of the road leading from” Site A” to “Site B”.

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B

A

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