I was curious what the R-C time constant is, for a conventional storage-tank style electric water heater; I came up with an answer that seems very counter-intuitive.
("RC time constant" is the product of a resistance and capacitance, with the dimensions of time. In that time, a given capacitance C is charged or discharged, through a given resistance R, about 63%. For thermal systems, R can have the dimensions: degrees-F per btu per hour and C the dimensions: btu per degree-F).
For my 10 gal kitchen water heater, the surface area of the tank is about 8 sq-ft, and the insulation is about 8 sq-ft * degree-F per btu/hr (aka. R-8). Thus the overall thermal resistance of the tank's envelope is about 1 degree-F per btu/hr.
The thermal "capacitance" is about 80 btu per degree-F (10 gals of water at 8 lbs per gallon, with a btu defined as the energy to raise one lb of water by a degree-F).
Thus the thermal R-C time constant is (1 degree-F per btu/hr) * (80 btu per degree-F), or 80 hours. That means that in 3+ days, after losing power, the tank would still retain 37% of its heat (or cool only 63% of the way from its set temperature to ambient temperature). Maybe that's right, but it seems pretty counterintuitive. Am I calculating wrong somehow ?