I'm trying to size (in watts) a heater to heat a glass of water from ambient (Ti) to a certain temperature (Tf) in a given time period (say, 1 hour). The heat-loss from the glass at Ti is 0 watts. The heat-loss from the glass at Tf is Y watts. I'm assuming that the heat loss increases linearly between Ti and Tf (I hope this is reasonable). The energy needed (assuming no heat-loss) to heat the water from Ti->Tf in 1 hour is X watts. Naturally, I can size the heater to be (Y + X) watts. However, this will heat the water up faster than necessary because initially there will be no heat-loss from the glass. Is there a clever way to more accurately size this heater? Thanks for your time.