I was taking a shower this morning, and I wondered how much it actually cost to heat each gallon of water as I was using it, so I got on the internet and looked up some handy unit converters and came up with some numbers.
First, the assumptions.
Assume 33.3 C rise in temperature of the water.
Assume $.10 per kWh of electricity.
Assume my shower head uses one gallon per minute.
Actually, the last two assumptions are known quantities, only the first one is a real assumption, based on raising the temperature from 50F to 110F. In the summer time, the temperature raise is lower, in the winter it is higher, so it's an estimated average.
Anyway, I came up with about 1.5 cents per gallon. Combine that with 2 cents per gallon for the water and I get 3.5 cents per gallon, that means if I take a 6 minute shower, it costs me 21 cents, or twice that for my wife.
If we were using the old tank water heater, it would be different, we'd have to add at least one third for the inefficiencies of the heater itself, then add additional costs for the temperature loss over 60 feet of copper tubing under the house.
So, now we know how much it costs to take a shower.