How much energy does it take to heat water for a 15-minute shower and what is the cost?
The cost of the thermal energy required to heat water can be calculated if the flow rate and the required temperature rise are known. For example, standard showerheads typically have a flow rate of 2.5 to 3.0 gallons per minute (gpm), while low-flow models have a flow rate of 1.2. to 2.0 gpm.
Incoming potable water temperature is assumed to be 50°F. For most uses, the water heater temperature setting is 120°F, but can be as high as 140°F. For a shower, a typical temperature of 105°F is achieved with a combination of hot and cold water.
A British thermal unit (Btu) is defined as the amount of heat required to raise the temperature of one pound of water one degree Fahrenheit. Since a gallon of water weighs 8.34 pounds, the flow rate (gpm) can be converted to pounds for the specified time use, and then converted back to Btu.
The total Btu required for a 15-minute shower with a 2.5 gpm showerhead can be calculated as follows:
The amount of heat required = Water Volume (lb) x Temperature rise (°F) x 1 Btu/lb°F
Water Volume (lb) = 2.5 gal/min x 15 min x 8.34 lb/gal = 313 lbs
Temperature rise from 50°F to 105°F = 55°F
The amount of heat required = 313 lbs x 55°F x 1 Btu/lb°F
= 17,215 Btu required to raise 313 lbs of 50°F water up to 105°F
If the gas water heater efficiency is 68 percent, then 25,316 Btu (17,215/0.68) is required from the heating source to supply the thermal energy for this 15-minute shower. At a cost of $1.00 per 103,000 Btu, the water heating cost is approximately $0.25.
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