Is "eco" shower mode actually using less power? At work we have electronic showers in the gym, they have three modes:


*

** (A snowflake, Which I guess means no heating at all)

*| eco (A Bar and eco)

*|| (Two Bars... so full power I guess)


The shower also has a temperature readout in degrees Celsius. 
There is no water pressure change between modes. The difference between | eco and || appears to be the number of heating elements used to heat the water (1 or 2 repectively). 
I was recently reprimanded for using the shower on || full mode instead of | eco, though the temperature I was showering at was what I usually aim for (38 degrees C, also I left the shower switched to || after I'd got out, which is how I was found out...). 
So counter intuitively, am I saving energy by using || mode and having two elements at a lower temperature heating the water, or is having only a single, hotter element really using less energy to heat the water?
I was under the impression that the higher the temperature of the element, the less efficient it was (higher resistance), and also the increased surface area would mean more efficient heat transfer.
 A: Heaters are one of the very few devices that are 100% efficient. All of the energy we put into them ends up as heat (though not all that heat may go where you want it to).
So to a first approximation the energy used by your shower is determined by how hot you run the water and for how long, and it doesn't matter what heat setting you use. I say to a first approximation because there could be small effects e.g. a high heat setting may actually boil the water and some heat could escape as steam rather than heating the water.
But remember there's a human at the end of this. Human perception of heat tends to be relative, and if you use a lower heat setting it's likely you will shower in cooler water possibly without noticing. If you do notice the water isn't as hot you probably won't shower for as long. So for the person paying the electricity bill using a low heat setting is a win - though possibly not for you.
Re your comment:

I was under the impression that the higher the temperature of the element, the less efficient it was (higher resistance), and also the increased surface area would mean more efficient heat transfer.

Note my first paragraph. Assuming thermal equilibrium, all the heat dissipated in the heating element goes into heating the water. If this wasn't the case the heating element would get hotter, and the rate of heat flow would increase, until the energy in and energy out balanced again. The exception would be if the element got so hot that it boiled the water and heat was lost as steam (though I suspect you'd notice if the water was that hot :-).
So it doesn't matter if you have one hot element or two cooler elements. The electrical energy consumed by the shower unit will still all end up as thermal energy in the water.
