March 13, 2006
Science A52 Section 5
Problem 1: Understanding of magnitude of energy units
How many light bulbs must be kept on for an entire month in order for a house to consume 150 therms of energy. Assume 4 weeks in 1 month and light bulbs with a power rating of 60 W.
Problem 2: Heating value calculation
Consider a 250 MW power plant burning coal. The net power plant efficiency is 33 %, and the heating value of coal is 28,400 kJ/kg. How much fuel must be supplied to this plant per day when it is running at full capacity?
Problem 3: Hydroelectrical plant
On the American side, the Niagara falls are 54 meters high. 75,000 gallons of water flow over the American falls each second, amounting to only 10% of Niagara's total water flow. Assume that all of the waterfalls at Niagara are at the same height as the American falls. Density of water= 1000kg/m3 and there are 264 gallons per 1 m3.
(a) What electric power can possibly be obtained by allowing all of the water in the Niagara waterfalls to flow through a hydroelectric plant. Assume that the hydroelectric plant would have an efficiency of 80%.
(b) Assuming the tourism revenue is $300 million per year and the cost of energy is 10cents/kWh, would it make economic sense to set up a hydroelectric plant at Niagara?
Problem 4: Hydroelectrical power
A hydroelectric plant has an electrical capacity of 150 MW. The operating head is 35 m, and the water flow rate into the turbines is 500 m3/s. Determine the overall efficiency of this plant under these conditions. The density of water is 1000kg/m3.
Problem 5: Energy from wood
From Prof. McElroy’s handout we see that the energy in wood is roughly 20 million BTU per cord which weighs ~ 4000lbs.
(1) Assuming that an average tree weighs 2000lbs after seasoning (drying), and that the average human consumes 330 million BTU each year, how many trees would you have to use per year? How many lbs per day?
(2) Next, you’re thinking of buying a wood fueled hot tub (common in New England). The hot tub holds 600 gallons. Assume that on average you will have to heat the tub from 50 degrees to 115 degrees Fahrenheit for each use and that 1 gallon weights 8.33 lbs. What fraction of a tree with this take assuming 20% efficiency?
(3) Assume that you plan on using this hot tub 2 times per week for a whole year. How many trees would you consume in a year? How much energy would this use?
(4) According to Prof. McElroy’s accounting, how much forest would you need to sustainably supply this much energy? Assume that one acre supplies 14 million BTUs per year.