# Efficiency of Scaled-Up Electric Water Heater Elements



## Eric Johnson (Mar 23, 2007)

Here's a simple question that there seems to be some disagreement on:

Is a scaled-up water heater element less efficient than a clean one?

Alliant Energy, Wisconsin's electric utility, recently ran a television segment on water softeners, in which they claimed that scale cuts into efficiency. I don't think that's true. While a scaled-up element will certainly overheat and fail before a clean one, it seems to me that all of the electricity going to the element results in heat, which eventually finds its way into the water. It may take longer to heat the tank, but it won't draw more juice in the process.

The story is completely different with a gas or oil-fired water heater, of course, since heat that is not absorbed by the water in the tank goes up the stack. But with electricity, efficiency is lost in the form of heat, which in the case of a water heater, is all good.

No?


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## TMonter (Mar 23, 2007)

It does slow the rebound time of the tank when it's fouled and could reduce the heat transfer rate and therefore efficiency.  I don't think you'd see much impact on the overall thermal efficiency.


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## Harley (Mar 23, 2007)

Without putting words in your mouth, Eric....  It kindof sounds like you are saying the scale acts as "mini heat storage points"? to keep heat in the area, which would result in less cycling of the heating unit?


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## Eric Johnson (Mar 23, 2007)

I'm not advocating it. What happens, I think, is that the scale insulates the element, slowing the heat transfer. As TMonter says, you'd have a less responsive water heater, but not one that drew more electricity than a clean one. So while there are many reasons to install a water softener, cutting your electric bill ain't one of them.


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## Harley (Mar 23, 2007)

That does make sense


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## GVA (Mar 23, 2007)

Hard to explain but I used to work on extrusion systems and still work with heater's and controllers and the heater for an extruder (or just a stick/plate heater) if not fastened tight to the extruder it would burn cherry red and fry itself.  Same as if you turned on a new water heater and didn't have water in it...
The transfer of energy is important.  So I guess they are trying to say that the scale is actually insulating the element from the water and burning it out...  Though I'm not really sure what they are trying to say I've told my mechanics in the past to make sure heater plates are secured to what they are trying to heat...

I can imagine water heaters are the same.
EDIT
In rereading the original post, the efficiancy is affected because the heat isn't transfered to the water as rapidly as it should be...
thus wasting electricity to heat the same amout of water to a certain temp.


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## keyman512us (Mar 23, 2007)

Eric:


> The story is completely different with a gas or oil-fired water heater, of course, since heat that is not absorbed by the water in the tank goes up the stack. But with electricity, efficiency is lost in the form of heat, which in the case of a water heater, is all good.
> 
> No?



Without going into an entire "Science/math class lesson of E=IxR, etc,etc"...which is the last thing I want to get into...since it's "after frosty-thirty"(beer drinking time). Electrical efficiency with CONDUCTORS and WINDINGS is lost in the form of heat...with a heater element it is a whole other ballgame. The properties start to change, so does current flow and heat (transfer). Even though I doubt you would notice a difference in the light bill...it still isn't optimal.


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## DiscoInferno (Mar 23, 2007)

I think the bottom line is that if we exclude heat loss from the tank via radiation/conduction/convection, then the electric power into a submerged heating element has nowhere to go but into the water.  Such a unit should always be essentially 100% efficient.  I don't think that the scale will change the resistance of the element significantly, so the power delivered will be constant.  It's just that the equilibrium temperature of the partially insulated element will be higher.  It is possible that the element resistance has a weak dependence on temperature, but this would only affect the rate of power (heat) transfer, not the efficiency.


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## babalu87 (Mar 23, 2007)

Can I try and sum it up fairly quickly with an analogy?

A 100 watt lightbulb left on for 10 minutes uses more energy that one left on for 5 minutes.

The water heater has to run longer to heat the same volume of water with the "dirty" element correct?


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## Eric Johnson (Mar 23, 2007)

The lightbulb's job is to produce light, not heat. The heat it does produce is lost efficiency. 

The way it was explained to me (and I don't know, which is why I'm asking) is that the heat output of electricity in a heating coil is limited to about 3,400 btu per kw hour. So, while it may take longer to generate the same amount of heat, it will draw the same amount of electricity over that time period.

Put another way, the draw depends on the load. Less load (i.e., a restricted ability to transfer heat) means less draw.

I agree with Disco--electric water heaters are 100% efficient, by definition. Where else can the energy go? It's either being restricted, or it's being transferred into the water, or its busy burning up the element (and generating heat in the process). It's not going to ground. It has to manifest itself as heat. Less heat production (in this case) per hour translates into less power consumption.


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## elkimmeg (Mar 23, 2007)

How to off set elememt heat loss insulate the crap out of the tank and the hit water transimmion pipes


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## Andre B. (Mar 23, 2007)

Depends on the amount of scale.

If it is just a coating on the elements then the heater will run a little longer before the water temp is high enough for the stat to switch off.  The elements inside the scale will be hotter at this point then they would be without the scale, this heat will continue to heat the water.  This will cause the temperature of the water to overshoot the stat setting by more then it would with clean elements.
These higher temperatures will increase heat loss thru the insulation.

With just a thin coating say under an inch or two the effect in small but with real bad scaling like where the scale completely fills the lower parts of the tank it will have a very noticeable effect.  I that case the heat will be coming from the element thru the scale and direct to the tank wall with only a small part of it getting to the water.

A friend and coworker replaced his 40 gallon electric water heater with a 40 gallon electric water heater two years ago and his bill dropped $75 a month. When he got the old one out of the basement (not an easy task) he cut it open and found that there was about 30 gallons of lime scale in the tank.;0


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## jjbaer (Mar 23, 2007)

Andre B. said:
			
		

> Depends on the amount of scale.
> 
> If it is just a coating on the elements then the heater will run a little longer before the water temp is high enough for the stat to switch off.  The elements inside the scale will be hotter at this point then they would be without the scale, this heat will continue to heat the water.  This will cause the temperature of the water to overshoot the stat setting by more then it would with clean elements.
> These higher temperatures will increase heat loss thru the insulation.
> ...



that's because in addition to heating the water he was also heating the scale and that takes energy.  About 50% of the fuel cost goes to simply maintaining the water temp.


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## Eric Johnson (Mar 23, 2007)

See, that's where I'm confused. The heat that goes into the scale eventually makes its way into the tank, albeit more slowly. In fact, any energy going to that heating element has to wind up in the tank. There's no place else for it to go.

Not to confuse the issue, but if you have scale with a large amount of iron, a scaled-up element might even have a greater heat transfer, since the surface area is greater.


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## Andre B. (Mar 23, 2007)

castiron said:
			
		

> that's because in addition to heating the water he was also heating the scale and that takes energy.  About 50% of the fuel cost goes to simply maintaining the water temp.



No.

Read it again.

Edit:

The scale only gets heated one time after that the heat into and out of the scale must be equal.

The question is where the heat comeing out of the scale is going, into the water or direct to the tank walls.


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## Andre B. (Mar 23, 2007)

Eric Johnson said:
			
		

> See, that's where I'm confused. The heat that goes into the scale eventually makes its way into the tank, albeit more slowly. In fact, any energy going to that heating element has to wind up in the tank. There's no place else for it to go.
> 
> Not to confuse the issue, but if you have scale with a large amount of iron, a scaled-up element might even have a greater heat transfer, since the surface area is greater.



But that heat in the scale is delayed and if that delay causes the water temp to rise above what it would without the scale after the thermostat turns off the element the higher temperature difference between the water and the outside environment will result in greater loss thru the insulation until the water temp is back down to normal.

And if there is a lot of scale it can result in a thermal short circuit between the element and the tank wall, bypassing the water.


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## DiscoInferno (Mar 23, 2007)

Andre B. said:
			
		

> But that heat in the scale is delayed and if that delay causes the water temp to rise above what it would without the scale after the thermostat turns off the element the higher temperature difference between the water and the outside environment will result in greater loss thru the insulation until the water temp is back down to normal.
> 
> And if there is a lot of scale it can result in a thermal short circuit between the element and the tank wall, bypassing the water.



This does sound reasonable, if one has that much crud in the tank.  Clearly I was thinking on too small a "scale".   :coolgrin:


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## mikeathens (Mar 23, 2007)

I believe scale on the elements shouldn't cause too much (if any) loss of efficiency - only noise (crackling, popping).  Scale buildup in the tank, however, is a different story (that's why you're supposed to drain every month or so).   Part of that might be due to heating the scale (as already mentioned), the other due to essentially creating oversized heating elements when you lose volume in the tank.  Similar to using a 4 ton AC unit to heat a 400 sq. ft. apartment.  But, I'm not an expert, just a goofy engineer that likes to think he remembers stuff from his thermodynamics class 13 years ago.


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## Eric Johnson (Mar 23, 2007)

Scale in the tank, for the purposes of this discussion, is a whole different issue. The question is specifically directed at the heating element itself.

Obviously, tank insulation, the capacity of the tank compromised by scale accumulation inside, slower response time, premature element failure--are all valid concerns.

I'm not saying that scale not a bad thing for a water heater. What I am saying is that scale on the heating element itself has little or nothing to do with electricity usage.


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## mikeathens (Mar 23, 2007)

Eric Johnson said:
			
		

> Scale in the tank, for the purposes of this discussion, is a whole different issue. The question is specifically directed at the heating element itself.
> 
> Obviously, tank insulation, the capacity of the tank compromised by scale accumulation inside, slower response time, premature element failure--are all valid concerns.
> 
> I'm not saying that scale not a bad thing for a water heater. What I am saying is that scale on the heating element itself has little or nothing to do with electricity usage.



Isn't that what I said, too?  Sorry for mentioning scale in the tank.


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## DiscoInferno (Mar 23, 2007)

Eric Johnson said:
			
		

> What I am saying is that scale on the heating element itself has little or nothing to do with electricity usage.



Right up to the point where the element burns up, yes.


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## Highbeam (Mar 23, 2007)

Resistance is dependent on temperature. A cold element has the least resistance and the most current will pass through it. As the element heats up the resistance gets higher and the current through the circuit is reduced. A hotter element can run longer on a KwH than a cooler element. The element coated in scale will run hotter and longer since the scale insulates the hot element from the cold water but it will use less energy per hour since the current flow is less through the hotter element. I vote that at the end of the day the clean and dirty elements will have used the same number of kwH. 

Also a newer hot water heater will almost always use less energy than an old tank since the newer ones are better insulated.

Good thread.


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## DiscoInferno (Mar 23, 2007)

Highbeam said:
			
		

> Resistance is dependent on temperature. A cold element has the least resistance and the most current will pass through it. As the element heats up the resistance gets higher and the current through the circuit is reduced.



This is true, although I think for a typical heating element the variation over a wide range of temperatures is only a few percent.  An example of much stronger dependence is in incandescent lightbulb filaments, which tend to burn out when turned on cold because the initial resistance is much lower and the initial current is much higher than the operating current.


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## Andre B. (Mar 23, 2007)

Highbeam said:
			
		

> Resistance is dependent on temperature. A cold element has the least resistance and the most current will pass through it. As the element heats up the resistance gets higher and the current through the circuit is reduced. A hotter element can run longer on a KwH than a cooler element. The element coated in scale will run hotter and longer since the scale insulates the hot element from the cold water but it will use less energy per hour since the current flow is less through the hotter element. I vote that at the end of the day the clean and dirty elements will have used the same number of kwH.
> 
> Also a newer hot water heater will almost always use less energy than an old tank since the newer ones are better insulated.
> 
> Good thread.



I think you may be thinking of light bulbs.
Yes it changes some but for nichrome heating elements at temperature changes of only 70 degrees or so it is not much. Nothing like a tungsten light bulb going from room temp to 2200°C.

Some temperature coefficients ohms per degree C.
http://www.allaboutcircuits.com/vol_5/chpt_3/4.html

```
Nichrome  0.00017
Copper    0.004041
Tungsten  0.004403
```


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## DiscoInferno (Mar 23, 2007)

Andre B. said:
			
		

> Some temperature coefficients ohms per degree C.



To be really picky, the units are not Ohms/deg C, but just 1/deg C.  It's a scale factor, to be multipied by the temperature difference (to make it unitless) and then multiplied by the resistance (which already has units of ohms) at the reference temperature to get the resistance change.

So, a 1kW nichrome heating element would have a nominal resistance (at 20 deg C, say) of  (110V)^2/1000W = 12.1 Ohms.  At 120 degrees, it would have a resistance of 12.1 Ohm * (1 + 0.00017/deg C * 100deg C)=12.3 Ohm, and put out a power of (110V)^2/12.3 Ohm = 983W, a 1.7% loss of heating power.

If they made the element out of copper, then evidently the resistance at 120 deg C would rise to 17 Ohms, and the power would drop to 712 W.  Which is why they use nichrome I guess.


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## Andre B. (Mar 23, 2007)

DiscoInferno said:
			
		

> To be really picky, the units are not Ohms/deg C, but just 1/deg C.  It’s a scale factor, to be multipied by the temperature difference (to make it unitless) and then multiplied by the resistance (which already has units of ohms) at the reference temperature to get the resistance change.
> 
> So, a 1kW nichrome heating element would have a nominal resistance (at 20 deg C, say) of (110V)^2/1000W = 12.1 Ohms.  At 120 degrees, it would have a resistance of 12.1 Ohm * (1 + 0.00017/deg C * 100deg C)=12.3 Ohm, and put out a power of (110V)^2/12.3 Ohm = 983W, a 1.7% loss of heating power.



Yep let one slip there.
Now really picky would be if we get into linearity. 

Depending on the thermal resistance out of the heating element, a 120°C could give you a boiler instead of a water heater.


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## cbrodsky (Mar 24, 2007)

Andre B. said:
			
		

> Depends on the amount of scale.
> 
> If it is just a coating on the elements then the heater will run a little longer before the water temp is high enough for the stat to switch off.  The elements inside the scale will be hotter at this point then they would be without the scale, this heat will continue to heat the water.  This will cause the temperature of the water to overshoot the stat setting by more then it would with clean elements.
> These higher temperatures will increase heat loss thru the insulation.
> ...



Are you suggesting that the thermal conductivity of the scale is higher than water to somehow thermally bridge?  I would doubt that - water will already reach fairly efficient equilibrium with the inside tank wall.  The temperature drop should all be across the insulation around the tank wall.

I do agree on the first point under the assumption that the thermal conductivity through the scale is lower.  Then in that case, it will take longer to equilibrate the water temperature, in which case you may have a slight overshoot.  But I think that would still be getting into the noise in terms of overall efficiency.  I wouldn't expect a well insulated tank to suffer as a result of this.

-Colin


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## Andre B. (Mar 26, 2007)

NY Soapstone said:
			
		

> Are you suggesting that the thermal conductivity of the scale is higher than water to somehow thermally bridge?  I would doubt that - water will already reach fairly efficient equilibrium with the inside tank wall.  The temperature drop should all be across the insulation around the tank wall.
> 
> I do agree on the first point under the assumption that the thermal conductivity through the scale is lower.  Then in that case, it will take longer to equilibrate the water temperature, in which case you may have a slight overshoot.  But I think that would still be getting into the noise in terms of overall efficiency.  I wouldn't expect a well insulated tank to suffer as a result of this.
> 
> -Colin



Maybe not the best way of explaining what I am thinking.

How about this way.
If you start with a tank that holds 40 gallons of water and has a given amount of surface area.
As the amount of scale and sludge builds up the volume of water in the tank goes down but the surface area stays the same.

Actually I would guess the thermal conductivity of water may well be less then that of the scale. Compared to metals water is almost an insulator, otherwise stratified heat storage systems would not work.
This chart gives water a value of 0.58 and concrete a range of 0.9 - 2 .
http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

But water mainly moves heat by convection and water high specific heat capacity makes it very good for moving heat as long as the water itself can move.


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## cbrodsky (Mar 26, 2007)

Andre B. said:
			
		

> NY Soapstone said:
> 
> 
> 
> ...



I think the question in my mind is what is more rate limiting - heat transfer within the water/scale or heat transfer across the tank wall to the surroundings.  If both water and scale are orders of magnitude more efficient at conducting heat within the tank to the wall as opposed to the conduction out of the tank.  I think they are in a halfway decent insulated tank, then the difference between water or scale wouldn't have a material impact on overall heat loss.

Just curious - is the scale described a "wet" slurry on the bottom of the tank or is this a completely impermeable buildup on the heating element?  I've actually never owned an electric tank to see how they build up and where the crud exists, but I do hear about people "draining" them.

-Colin


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