Water Heating - Thermodynamics and Economics

Thermodynamics and Economics

Water enters typically residences in the US at about 10 °C (50 °F), depending on latitude and season. Hot water temperatures of 40–49 °C (104–120 °F) are usual for dish-washing, laundry and showering, which requires that the heater raise the water temperature about 30 °C (54 °F) if the hot water is mixed with cold water at the point of use. The Uniform Plumbing Code reference shower flow rate is 2.5 US gallons (9.5 L) per minute. Sink and dishwasher usages range from 1–3 US gallons (3.8–11 L) per minute.

Natural gas in the U.S. is measured in CCF (100 cubic feet), which is converted to a standardized heat content unit called the therm, equal to 100,000 British thermal units (BTU). A BTU is the energy required to raise one pound of water by one degree Fahrenheit. A U.S. gallon of water weighs 8.3 pounds (3.8 kg). So, to raise a 40-gallon tank of 55 °F (13 °C) water up to 105 °F (41 °C) would require (40 × 8.3 × (105 − 55) / 100,000) BTU, or approximately 0.17 CCF, at 100% efficiency. A 40,000 BTU/h heater would take 25 minutes to do this, at 100% efficiency. At $1 per therm, the cost of the gas would be about 17 cents.

In comparison, a typical electric water heater has a 4500 watt heating element, which if 100% efficient results in a heating time of about 1.1 hours. Since 16,600 BTU is roughly 4.9 kWh, at 10 cents/kWh the electricity would cost $0.49. Operating a shower at 2.5 gpm and 104 °F (40 °C) is equivalent to operating a 19.8 kW appliance . In the UK, domestic electric immersion heaters are usually rated at 3 kilowatts.

Energy efficiencies of water heaters in residential use can vary greatly, particularly based on manufacturer and model. However, electric heaters tend to be slightly more efficient (not counting power station losses) with recovery efficiency (how efficiently energy is transferred to the water) reaching about 98%. Gas fired heaters have maximum recovery efficiencies of only about 86% (the remaining heat is lost with the flue gasses). Overall energy factors can be as low as 80% for electric and 50% for gas systems. Natural gas and propane tank water heaters with energy factors of 62% or greater, as well as electric tank water heaters with energy factors of 93% or greater, are considered high-efficiency units. Energy Star-qualified natural gas and propane tank water heaters (as of September 2010) have energy factors of 67% or higher, which is usually achieved using an automatic flue damper or power venting. Direct electric resistance tank water heaters are not included in the Energy Star program, however, the Energy Star program does include electric heat pump units with energy factors of 200% or higher. Tankless gas water heaters must have an energy factor of 82% or higher for Energy Star qualification. Since electricity production itself today has efficiency levels ranging from only 15% to slightly over 55% (combined cycle gas turbine), with around 40% typical for thermal power stations, direct resistance electric water heating is typically the least energy efficient option. However, use of a heat pump can make electric water heaters much more energy efficient and lead to a decrease in carbon dioxide emissions, even more so if a renewable source of electricity is used.

A tankless water heater operating at those same power levels (at 100% efficiency) would be able to supply 1.6 gpm continuously, raising the temperature by 30 °C (54.0 °F). The same unit could supply 1.3 gpm while raising the temperature by 33 °C (59.4 °F). To handle a full house load of multiple uses (at least 5 gpm) with a centralized tankless water heater requires three to four times this power level—somewhat difficult to achieve with natural gas, and difficult to achieve with electricity. Many tankless water heaters can use over 100,000 BTU/h during high flow, and so require especially large power supplies.

Unfortunately, it takes a great deal of energy to heat water, as one may experience when waiting to boil a gallon of water on a stove. For this reason, tankless on-demand water heaters require a powerful energy source. A standard 15-ampere rated wall electric outlet, by comparison, only sources enough power to warm a disappointingly small amount of water: about 0.17 gpm at 40 °C temperature elevation.