Problem Assignment
Problem 1:
You own a small 40,000 sq ft warehouse and you use natural gas as a heating fuel. A neighboring warehouse uses heating oil to heat similar 20,000 sq ft. operation. You consume 800,000 cubic feet of natural gas, and your neighbor uses 5000 gallons of heating oil during the winter.
Which of you has used more energy to heat your operations? Is total energy consumption the correct comparison to make? If not, what is the best basis for comparison and on this basis, which is the most energy efficient operation?
Problem 2:
You are an executive for the local power company. The company's power generators will run on either natural gas or residual fuel oil. It is your job to switch the generators between the two fuels so that you are always using the less expensive fuel to keep costs down.
Your generators are currently running on natural gas but the price of natural gas is rising more rapidly than the price of residual fuel oil. Based on the fact that natural gas costs $8.50 per thousand cubic feet and residual fuel oil costs $70 per barrel, determine if you should switch to residual fuel oil or remain on natural gas.
3. You have been away on vacation and during this time the heater on your new hot tub has tripped. The water temperature is now 35oF and you want to bring it up 100oF. The hot tub measures 9 ft x 9 ft x 4 ft deep. (Hint: Determine the volume of the pool in cubic ft, look up how many pounds of water there are in a cubic foot and review the basic definition of a BTU.)
a) Assuming no energy losses, how much energy in BTU's will this require?
b) What is the equivalent energy usage in kWhrs?
c) Below is the heater unit on your hot tub. Assuming no heating losses, how long will it take to bring the hot tub up to 100oF
4. I have a 1000 Watt inverter than I can plug into my Prius so I can use it as an emergency generator to power part of my home during an electricity blackout. Assume that I draw, on average, 400 W to keep my heating system, refrigerator and a few lights running. How long could I keep these items running with 10 gallons of gasoline in the tank. Assume the conversion efficiency of gasoline into electricity of 28%.
5.) Look at your monthly electricity bill during the winter months. Depending on your consumption, calculate what size emergency generator, in kW, you would need to power your home. Assuming a 25% conversion efficiency of gasoline to electricity, how much gasoline would you consume in one month of generator usage.
6) A wind farm has a capacity factor of 28% and has twelve 2MW turbines and it can sell electricity for 6.5cents/kWh. How much revenue will this wind farm generate in one year?
7) The controlling body for electricity supply in New England, ISO-NE, has a winter reliability program which involves paying owners of oil fired generators to store oil during the winter months so that if there is a shortage of natural gas, these oil based units can be fired up to generate electricity.
With oil and having dropped so much recently, calculate the price of natural gas, in $/1000 cu. ft, that would be equivalent to burning jet fuel for electricity production at $60/barrel.
Assume the efficiency of electricity production from oil is 30% and the efficiency for electricity production from natural gas is 40%. Check your answer against the prevailing price for natural gas to make sure you are within the correct order of magnitude.