Question

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

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

(3) How much potential energy increase takes place when all this water was raised from a river at an average elevation of 200 meters so that the water in the upper reservoir has an average elevation of 300 meters. (Note: For simplicity, just take the height change of the water to be 100 meters from the river to the reservoir, thus neglect that some water moves from the river to a slightly different heights as the surface of the reservoir rises. This is what was meant by saying the water in the upper reservoir has an average elevation of 300 meters.)

(4) How much power will be available to a city from the reservoir if 2 % of the water (i.e., stored energy) in the full reservoir is drained in ½ hour through the turbine that generates electricity? To help to provide context for the answer you will get, there is a power plant located at Mt. Tom Junction (which you can see if you travel south on route 91 near where Easthampton meets Holyoke). It was recently decommissioned, but used to burn coal (1200 tons per day) to create steam to spin turbines to generate electricity and had an advertised power production capacity of 146 megawatts (mega = million). Such a water storage arrangement can be used to quickly supplement such a power plant when the needs for energy fluctuate, or when there is short-term high demand. This plant used to be able to provide more than twice the needs of the city of Holyoke.

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

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

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

(7) If it did this continuously for one year, how may joules of electrical energy could the coal-burning Mt. Tom power plant produce 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 talks about how much carbon dioxide is created when a ton of coal is burned. (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 plant burned bituminous coal (as opposed to some other kind), and compute how many pounds of carbon dioxide per year were introduced into the atmosphere by the Mt. Tom coal-fired power plant. Wind farms that replace coal-fired power plants help reduce greenhouse gasses (carbon dioxide). Just as a comment: a maple or birch tree that is 25 years old will absorb about 3 pounds of carbon dioxide from the atmosphere per year, but this depends on the type of tree. A 25 year old white or red pine will absorb about 14 pounds per year. Deforestation in various places eliminates the natural ability of such trees to clean the atmosphere. Take a look here http://wiki.answers.com/Q/Co2_consumption_by_rain_tree if you want more information (optional). To get a rough idea about personal energy use and the carbon dioxide emission that results, check out this nice little calculator and try to enter some values: http://www.carbonify.com/carbon-calculator.htm. Note that in the calculator some unstated assumptions are made, but it is a useful exercise. So, for example, using the calculator:

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

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

(12) Use the calculator to determine how many tons of carbon dioxide this oil use puts into the atmosphere each year. (Be careful to note that the calculator quantity column is in terms of per month.)

Answer 1