Conventional hot-water heaters consist of a tank of water maintained at a fixed

Question

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. Some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. No water tank is involved, so no heat is wasted. A typical household shower flow rate is 5.94×104 gal/min (9.41 L/min ) with the tap water being heated from 48.0 F (8.89 C) to 123 F (50.6 C) by the on-demand heater.

What rate of heat input (either electrical or from gas) is required to operate such a unit, assuming that all the heat goes into the water?

Explanation / Answer

Water coming per min = 9.41 L

mass of water = 9.4 kg/min = 9.41 kg / 60 sec = 0.1568 kg/s

deltaT = 50.6 - 8.89 = 41.71 degC

Heat supplies per second = m Cwater deltaT

= 0.1568 * 4186 * 41.71 = 27382.8 Watt

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