The energy consumption associated with a home water heater

Chapter , Problem 1.48

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The energy consumption associated with a home water heater has two components: (i) the energy that must be supplied to bring the temperature of groundwater to the heater storage temperature, as it is introduced to replace hot water that has been used; (ii) the energy needed to compensate for heat losses incurred while the water is stored at the prescribed temperature. In this problem, we will evaluate the first of these components for a family of four, whose daily hot water consumption is approximately 100 gal. If groundwater is available at 15 C, what is the annual energy consumption associated with heating the water to a storage temperature of 55 C? For a unit electrical power cost of $0.18/kW h, what is the annual cost associated with supplying hot water by means of (a) electric resistance heating or (b) a heat pump having a COP of 3.