I'm specifically thinking about lime/sedimentation at the bottom of water heater, and calcification of heating elements (and not possible thermal insulation deterioration).

It is very often claimed (by both government energy efficiency experts and water-heater sellers/service people - but without sound theoretical explanation, alas) that calcified heating elements in electrical water heaters would lead to much higher energy bills for water heating (numbers often wildly ranging from 30% to over 400% percent increase in electrical power bills), and that it is imperative that water heaters get serviced (usually suggested on yearly basis) to drain out sedimentation and clean/replace the heating elements primarily for that reason (among others).

but I'm looking for theoretical/physical explanation for that (or a denial).

Now, I can see why calcification on and around heating element is bad, as it would be acting as thermal insulation between itself and water, which would:

1. prolong the time needed for heating element to heat the full tank of water (due to slower transfer of heat)

2. reduce life of heating element (due to it overheating, as thermostat shutoff would be delayed due to previous point)

Which are both valid reasons for regular service. However, I do not see why it would case any increase in energy usage?

I've tried looking up, and as best as I can see, the law of energy preservation should hold up. I cannot see the energy being converted to anything other than heat due to calcification of heating elements? And it that heat was used by heater, it must get transferred to the water around it eventually, right?

I see two things happening if heating element gets calcified:

• as it is isolated from cold water around it and initial thermostat assumptions, it will overheat, which would increase its electrical resistance somewhat, and reduce it's power in Watts (for example from 2000W to 1500W), thus prolonging time needed to heat the water (and reducing its lifetime)
• the calcification/lime would act as a "wall" which would slow down the heat transfer (which would also prolong time by which whole tank of water would be heated); however that heat energy would not be lost, as the calcification itself would continue to give off that heat energy back to the water even after the heating element was shut off from electrical power by thermostat

Are those assumptions correct, and if so, am I missing something else? Where would such energy used by heater be wasted (not transferred to heated water)? Or is "irregular maintenance of water heater leads to higher energy bills" just very popular urban legend?

So, the question is "is it true that calcified water heater elements would use up more electrical energy, and if so, why"?

(note: I initially considered posting this in diy.SE which has a lot to say about water heaters; but as I seek theoretical explanation and not practical usage, physics.SE seems much better place. Also note: english is not my primary language, so some terms might be wrong; and my physics knowledge is at [or was, two or three decades ago] at high school level)