Drat, where's my Heat Transfer book?
Ah screw it, it's all the way out in the kitchen, maybe 20 feet away, and I don't feel like getting up just now. So here it is from memory. (Are any of my professors listening?
😀)
A thought exercise which may help:
1) Cut a hole in a box.
2) Put your junk (namely, a 40W light bulb) in the box.
3) Don't open the box.
....
Oh, and the box is perfectly insulated - NO heat can escape.
Turn on the light.
Eventually, you'll be able to melt the glass surrounding the bulb due to heat buildup inside that insulated container.
And "heat" is a bit of a funny term; in my Heat Transfer course, it took on a slightly different meaning than what is normally heard - there, "heat" refered to energy being transferred between two bodies. An object cannot have "heat," as it isn't transferring it to anything. But it does have energy.
So when those elements are turned on, energy flows into them. Resistance in the element converts the electrical energy into thermal energy, measurable as a temperature increase in the element.
Now that energy will want to go somewhere. If the element is in direct contact with water, that energy can be easily conducted away to the molecules of the water, which in turn lowers the temperature of the element.
But if the element is insulated by scale, the energy has to attempt to force its way through it. Less energy is able to do so, due to the low thermal conductivity of the scale. Result: The water doesn't heat as quickly, and the elements get hotter. And
that is where the "extra" energy is going - it's making the elements hotter than they should normally be.
Originally posted by: spidey07
You're missing the point of efficiency - amount of energy transferred over time (not to mention the constant loss I described). Imagine putting an insulator over the heating coils; that's not very efficient.
Efficiency is a simple ratio to compare input and output. Efficiency in the case of the water heater would not be concerned with time, but with how much energy it takes to heat a given quantity of water.
Water's specific heat capacity is 4187 J/kg-K.
So ideally, if you put 4187 joules into a kilogram of water, you'll increase it by 1°C.
The question with the water heater's efficiency is, if I put 4187 joules into the
elements, how much of that will go into the water? The second question concerns the water heater's insulation - how much of that energy in the water will
stay there, and for how long?
If you want to know how quickly it will heat the water, that's not so much a question of efficiency, but of effectiveness.
😛