Electricity is used to provide domestic hot water at 100 degree C. The water is

Question

Electricity is used to provide domestic hot water at 100 degree C. The water is supplied at 10 degree C, and may be heated either with an immersion heater or with an ideal heat pump which extracts heat from the surroundings at 10 degree C. Compare the power consumptions when (a) the immersion heater is used, (b) the heat pump supplies heat to the hot water tank so as to keep it at 100 degree C, (c) the heat pump heats 'packets' of water from 10 to 100 degree C and then adds them to the hot water tank as required.

Explanation / Answer

Heat capacity of water = 4.184 joul/gm-oC. So the heat required to heat 1lit of water from 10 to 100 deg C is (4184x90) = 376.56 joule

a). Immersion heater converts directly electrical energy to heat energy through (I2 x R) where I is the current and R the resistance of the Immersion rod. As it converts directly the elctrical energy to heat energy and so the electrical efficiency is over 95%. The Power consumption will be highest. among all the three options.

b). Heat Pump work on Carnot cycle principle and it is reverse of the refrigeration where the heat is pumped from out side to inside the water and electrical energy is used for only pumping in the heat and so usually Electrical efficiency is few times higher. As the entire water is kept heated at 100oC and mixing is done at the tap level and so there will be higher conductive and convective losses than the option three. So, electrical efficiency will be better than direct heating in option 1 but inferior to option 3.

c). In this option again we are using the heat pump to transfer the energy from outside to inside of the tank but we keep only limited water heated at 100oC and based on use it is mixed in the tank to raise the tank water temperature. Here not only the size of the pump will be smaller but also losses due to conduction & convection will be less and so will be more efficient among all the three options.

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