Question

If you leave in Northern Florida that the annual average temperature outside changes on the minimum to 40 F and Summer to 80 F, to save energy, is it better to turn off your water heater and turn it on 1 hour before shower or use, or let it to be on all the time. The water set temperature is normally around 110 F. Show with detail calculations if there is any energy saving.

Answer 1

Solution:

Heat transfer, Q = M x S x ΔT

where,

M = Mass of water

S = Specific heat capacity of water

ΔT = Change in Temperature

Water set temperature Tf = 110 F

Consider Winter Case: Min. temp of water, Ti= 40 F

ΔT = Tf-Ti = 110-40 = 70 F

Consider Summer Case, Min. temp of water Ti= 80 F

ΔT = Tf-Ti = 110-80 = 30 F

Now, we consider that water heater is ON all the time - Case A

In this case, as the ΔT is positive in summer and winter, though the water is heated till temperature Tf, it will get cool down to Ti and again heater will get ON to keep the water temperature to Tf. Hence, it is advised to switch ON the water heater one hour before shower or use.

Assuming that it is one time use per day & if heater is ON continuously water gets cooled to Ti within 2 hours from Tf= heater will be operated between Ti and Tf for 12 times a day

Energy saved per day (Summer), Q = (12-1) xM x S x ΔT = 11 x 1 kg x 4.179 KJ/kg K x (30-32+273.15) K = 12464.49 KJ

Energy saved per day (Winter), Q = 11 x 1 kg x 4.179 KJ/kg K x (70+273.15-32)K = 14303.25 KJ