Just to stoke up the discussion about heat loss from an electric (or gas) hot water tank/heater, versus those instant-on type, herewith some current numbers.
Left the house at around 2.00 PM Thursday Sept 4th. turning off both the water supply and the circuit breaker for the electric hot water tank. Returned today, Sept 9th. at around 2.00 PM and noting that water was still quite warm, after an absence from a completely vacant house except for neighbour checking, of 5 days, measured the water temperature.
It was 80 deg F.
The foam insulated 40 US gallon tank is located in the basement which has an air temperature at this time of year of about 60 deg F. The water is normally heated to about 150 deg F.
So in 5 days the 40 gallons lost heat to the 60 deg. basement dropping in temp by 150 - 80 = 70 degrees.
Leaving aside for the moment that the 'rate' of heat loss was probably directly proportional to the difference in temperatures; i.e. highest at the start when the tank was at full temperature, what are members opinions on the following.
40 gallons x 8.33 = 333 pounds of water. 333 x 70 = 23,324 BTUs of heat lost during the 5 days. 23,324 / 3.41 = 6,840 watts of electricity. Previously used to heat water. 6,840 = 6.84 kilowatts of electrcity Which at 0.1 $ per k.watt hr. is/was a heat cost of 68.4 cents. 68.4 / 5 = 13.6 cents, per day. So at a rough approximation 14 cents per day (from a tank that was cooling down gradually over the 5 days). When the same tank is being maintained at 'normal' full temperature the heat loss; could we assume no more than twice that? Perhaps of the order of say 25 cents per day? **
Maybe someone with better mathematical skills could to do a more informed calculation? Using dy/dt etc. Also btw anything wrong with the numbers used?????
** Also noting that during the winter at least, the lost heat adds very slightly to warming this all electric house which consumes a year round average of about $8 per day (all costs including sales taxes included). Again, just hypothesising, if heating is say 60% of the $8 (say $4.80?), the rest being hot water, lighting computers, TV, radio, work shop etc. (some of which also aid heating) then the 'lost' heat from the hot water tank is of the order of, say 0.25 / 4.8 = about 5% of the house heating cost! i.e. Not very significant?