Suppose that we have a reservoir that has a surface area of 50acres, with an average depth when full of 15 meters. [Conversion: 1acre = 4096.86 square meters] If the reservoir were to start outwith a depth of 0 meters and eventually be filled to a depth of 15meters, (1) how much volume of water will have been added in thefilling of the reservoir from 0 meters depth to 15 metersdepth?

(2) What mass of water does this added volume of water have?

(3) How much potential energy increase takes place when all thiswater was raised from a river at an average elevation of 200 metersso that the water in the upper reservoir has an average elevationof 300 meters. (Note: For simplicity, just take the height changeof the water to be 100 meters from the river to the reservoir, thusneglect that some water moves from the river to a slightlydifferent heights as the surface of the reservoir rises. This iswhat was meant by saying the water in the upper reservoir has anaverage elevation of 300 meters.)

(4) How much power will be available to a city from thereservoir if 2 % of the water (i.e., stored energy) in the fullreservoir is drained in ½ hour through the turbine that generateselectricity? To help to provide context for the answer you willget, there is a power plant located at Mt. Tom Junction (which youcan see if you travel south on route 91 near where Easthamptonmeets Holyoke). It was recently decommissioned, but used to burncoal (1200 tons per day) to create steam to spin turbines togenerate electricity and had an advertised power productioncapacity of 146 megawatts (mega = million). Such a water storagearrangement can be used to quickly supplement such a power plantwhen the needs for energy fluctuate, or when there is short-termhigh demand. This plant used to be able to provide more than twicethe needs of the city of Holyoke.

On this related web site,(http://www.northfieldrelicensing.com/Pages/Northfield.aspx ) notethat the specifics of the energy storage system used by this powerplant at its Northfield site are similar to the case we havecalculated here. (5) On that site, see how many megawatts of power(Powerhouse section - historic station capacity) can be deliveredby the Northfield reservoir when the water flows down through atotal of four turbines. What is that number? Be careful to get yournumber from the section of the web page that mentions the fourturbines and the historic capacity.

Now this Mt. Tom power plant used to use 1200 tons of coal perday to create 146 megawatts of power. As noted, the coal is burned,heats water to make steam, the steam turns turbines and electricityis generated. Other things can turn turbines. For example, awindmill has a set of blades that cause the shaft to which they areattached to turn when the wind blows. This shaft turns a turbineand that generates electricity. Let’s take a look at a farm of suchwindmills. There is an approved project to create a windmill farmoff the coast of Cape Cod in Nantucket Sound. It is said that thewindmill farm will generate 1,491,384 megawatt hours of energy pertypical year. Recall that the kilowatt hour is a unit of energy. Sois the megawatt hour, it is just bigger.

(6) So, how many joules of energy will this be per year? Thatfossil fuel power plant at Mt. Tom Junction produced 146 Megawattsof power.

(7) If it did this continuously for one year, how may joules ofelectrical energy could the coal-burning Mt. Tom power plantproduce over the entire year?

(8) Compare this number with the one you got for the wind farm.Is the number roughly comparable? Here is a web site that talksabout how much carbon dioxide is created when a ton of coal isburned.(http://wiki.answers.com/Q/How_much_carbon_dioxide_does_a_ton_of_coal_produce)

(9) Look at that site, presume that the Mt. Tom power plantburned bituminous coal (as opposed to some other kind), and computehow many pounds of carbon dioxide per year were introduced into theatmosphere by the Mt. Tom coal-fired power plant. Wind farms thatreplace coal-fired power plants help reduce greenhouse gasses(carbon dioxide). Just as a comment: a maple or birch tree that is25 years old will absorb about 3 pounds of carbon dioxide from theatmosphere per year, but this depends on the type of tree. A 25year old white or red pine will absorb about 14 pounds per year.Deforestation in various places eliminates the natural ability ofsuch trees to clean the atmosphere. Take a look herehttp://wiki.answers.com/Q/Co2_consumption_by_rain_tree if you wantmore information (optional). To get a rough idea about personalenergy use and the carbon dioxide emission that results, check outthis nice little calculator and try to enter some values:http://www.carbonify.com/carbon-calculator.htm. Note that in thecalculator some unstated assumptions are made, but it is a usefulexercise. So, for example, using the calculator:

(10) If you drive an average medium sized car and drive 600miles per month, how many tons of carbon dioxide do you put intothe atmosphere per year? (Hit enter after you put 600 in the boxfor an average car.)

(11) At the bottom of the calculator, read off how many averagetrees are needed to offset this driving and reabsorb the carbondioxide. As another example, my house typically requires about 1400gallons of heating oil over the year.

(12) Use the calculator to determine how many tons of carbondioxide this oil use puts into the atmosphere each year. (Becareful to note that the calculator quantity column is in terms ofper month.)