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I'm still working on a simple equation to show the rate of heat loss off still water with a different delta t. But in the meantime, a thought struck me. Don't worry, it happens several times a year and I wasn't hurt this time....A practical way of looking at this would be to do a simple calc of the cost of running the heater. For the sake of this flimsy example, let's use a one-hour soak.If you have a 5000 watt heater, it will cost you a little over 5KWH (kilowatthours) to run for one hour. If you are paying $.25 per KWH, then your heater will cost $1.25 to run for an hour. I think a Quarter is a high rate, most non-California residents pay less.Just for fun, imagine a spa with very low temp difference between water and ambient air. The heater may run for as little as ten minutes out of the hour.That would be 1.25 / 6 or $.21 to run the heater for that one-hour soak.So, the higher the temp differential between water and air, the longer the heater will run. Keep in mind that in extremely low air temp situations, the heater may run for more than an hour for a one-hour soak - taking a few minutes AFTER the lid is closed to get back to the heat setting - but I think that would only happen in extremely cold climates, and nobody with any sense would live there.
At $.25/KW hour USD, you'd have to be crazy to live where you do! I pay $.085 CDN
Saturday morning I too was having an early morning soak in 103-degree water, feeling the fall chill in the air, when a bug of some kind landed in the spa. As I watched closely, he struggled between life and death in the hot water and I wondered if he was more frightened by the hot water or the fact that he was drowning.... Suddenly I had what most of you would call an "epiphany" and I knew clearly what I had to do........STOP DRINKING BEFORE NOON!
I was halfway through this topic and my head started hurting so much I had to retract that vow!
Ok so at any point does the body temperature of the soakers enter as a variable? For example: if you have 6 soakers with body temps of 98.6 and we are trying to keep the water at 102, do the soakers actually have a downward influence on temp? Conversely, If you put 6 slightly feverish people with a temp of 100, and you trying to keep the water temp 95, would they raise the temp... and.... at what ambient air temp could you drop to where the 6 bodies would maintain the temp. of the water at 95?