On 29-Mar-2004, Bill Vajk wrote:

Ideally, yes. I do wonder, however, what the startup cost of
the electric heating element(s) is. A higher cycling rate
isn't going to present a linear extension based on delta T
alone since the current consumed during the period the
heating element takes while coming up to operating temperature
is higher than at near steady state operation.

That doesn't matter at all to the total energy usage.

If the average water temperature is stable over a long period (small
fluctuations don't matter), then the total energy going into the tank during
this time must exactly equal the total heat energy lost from the tank. This is
a consequence of the law of the conservation of energy. If we put more energy
in, the water temperature will rise over time; if we put in less, the
temperature will fall. If it is stable of an extended period, then the total
energy put in during that period must match the energy taken out. (If you find
a tank that violates this law, explain why and immediately apply for a Nobel
prize.)

So regardless of the voltage, amps, wattage, size or shape of the heating
element, as long as the heater is able to supply enough energy to match the
loss (76 watts in my case), the total energy used over a long period will be
the same; but the duty cycle will change. You could put a 76 watt heater
inside the tank, and it would use the same long-term energy as a 4500 watt
heater. It would just have a longer duty cycle -- 100% rather than 1.6%.

The water temperature, as it rises, results in successively
higher operating temperature of the heating element with a
corresponding (albeit small) decrease in the current drawn.
I don't know what the typical slop in the thermostat
temperature is for an electric hot water heater.

Irrelevant, it just changes the duty cycle -- the long term energy use is
exactly the same.

Conservation of energy -- Not just a good idea, it's the law.