A solar hot water system for a home will cost $5,000 installed. You currently us
ID: 1714450 • Letter: A
Question
A solar hot water system for a home will cost $5,000 installed. You currently use 200 gallons of hot water per day, which has to be heated from 50 oF to 120 oF.
a) Figure how many BTU that much water will take to do this heating every day?
Remember that to create heat, 3,410 BTU = 1 kWh. From this data and the heat capacity of water ( 1 BTU per every pound of water heated 1 deg F) you should be able to calculate the total heat energy (the total BTU's) needed to warm that much water (200 gallons = 1,600 pounds of water) each day, and add a bit more energy to keep it hot, say 20%, since it cools off and re heats during each day while it is sitting waiting to get used. Then convert that heat energy (BTU) to Kilowatt hours needed from the utility to DO it.
b) Assume an average cost of electricity of $0.15/kWh what will be the total money spent on heating this water the regular way in a year?
c) If you did spend the $5,000 on the new solar system, what is the simple payback ( the number of years to break even)?
Don't worry about FCR or AOM. We assume it stays leak free until its paid for and that you had the cash to do this without borrowing any money.
Explanation / Answer
Water used per day =200 gallons = 1600 lbs
Temperature difference between heated water and ambient water = 120- 50 = 70 degree fareinheit
Energy in BTU required to heat 1 lb water by 1 degree fareinheit = 1 BTU
Answer a
BTU required to heat 1600 lbs water by 70 degree fareinheit ( Without additional requirement to keep hot ) = 1600 * 70 = 112000 BTU
BTU required considering 20 percent additional requirement = 1.2 * 112000 = 134400 BTU
Thus energy in KWH = 134400 / 3410 = 39.41 KWH
Answer b
Average cost of electricity = $0.15 / KWH
Thus total cost spent per day = 0.15 * 39.41 = $ 5.9115
Considering average of 365 days in a year total money spent in year = 365 * 5.9115 = $2157.6975 say 2157 $ per year
Answer c
For breakeven
Cost of solar plant = $5000
Cost spent on heating water per year = $2157
Thus money saved per year by using solar plant = $2157
Neglecting any rate of return on money if deposited
No. Of years for breakeven = 5000/2157 = 2.32 years
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