On-Demand Water Heaters. Conventional hot-water heaters...

On-Demand Water Heaters. 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 drawbacks are that energy is wasted because the tank loses heat when it is not in use and that 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 9.0 $\mathrm{L} / \mathrm{min}$ with the tap water being heated from $10^{\circ} \mathrm{C}$ to $45^{\circ} \mathrm{C}$ 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?

Key Concepts

Specific Heat Capacity

This is a physical property that indicates the amount of energy required to raise the temperature of one unit of mass of a substance by one degree Celsius (or Kelvin). In heating applications, knowing the specific heat capacity of a material (like water) is fundamental for calculating the energy needed to achieve a desired temperature change.

Mass Flow Rate

Mass flow rate refers to the amount of mass passing through a given point per unit time. In the context of heating water on demand, it is essential to determine how much water is being heated per second so that the correct amount of energy can be delivered to raise its temperature appropriately.

Temperature Change

Temperature change is the difference between the initial and the final temperature of the substance being heated. This difference directly impacts the total energy required, as a larger temperature change demands more energy to achieve.

Heat Energy Calculation

This concept involves determining the total energy required to heat a substance by using the formula that multiplies mass, specific heat capacity, and temperature change. It is central to understanding how much energy must be supplied by a heating unit over time.

Power

Power is defined as the rate at which energy is transferred or converted. In the context of an on-demand water heater, it quantifies how quickly energy must be supplied (in watts) to raise the water temperature effectively as it flows through the system.

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