I've got a hot tub in my garden with 1,500 litres of water in it and the target temperature is 38° centigrade.

The tub has two operating modes:

  • Economy: circulate water twice for 3 hours within 24 hours (at 4AM and 4PM). While circulating, heat if necessary.
  • Standard: same circulation but heat whenever temperature is dropping below 38°

Outside temperatures over here very between -15° at night (winter) and all the way up to +35° during the day (summer).

Usage of the hot tub is typically during the evening hours, the rest of the time the tub is covered with an insulated lid.

I observed that on warm days the economy mode consumes considerably less energy but I wonder if that will be true for colder days too and I would like to understand why this is the case.

I understand that the same amount of energy is needed to heat water, no matter how it's done. But isn't hotter water cooling down faster than cooler water? Does that have an impact on the decision of the mode?

Is it right that in an ideal world (which we don't live in), both modes should use exactly the same amount of power?

  • $\begingroup$ Yeah, that's it! :-) $\endgroup$
    – Krumelur
    Jul 26 '17 at 10:17

From your description, it sounds like "standard mode" keeps the water always at approximately 38 degrees, whereas "economy mode" lets the water get cooler than this often.

When the water is cooler than 38 degrees, there'll be less conduction out of the pool, as the temperature differential between the water and the surroundings is lower. Less heat loss means less heat that you have to pay to add.

So, unsurprisingly, "economy mode" will work out cheaper for you than "standard mode".

  • $\begingroup$ But doesn't it always take x watt hours to heat water by 1K? So in economy I have to heat up by maybe 8 degrees twice a day and with standard I have to heat 1 degree eight times? $\endgroup$
    – Krumelur
    Jul 26 '17 at 9:50
  • $\begingroup$ @Krumelur One is constantly circulating, the other does it for 6 hours a day. Thats already less power. The wamer you leave it the more heat it loses. In winter, it will be even worse to keep it warm all the time. In that mode you have to constantly supply the heat losses due to temperature difference. In the method when you allow it to cool, the heat out will decrease with time, so when you go to add the heat back , it's going to be less heat than it would have taken to maintain the full temp 24/7. $\endgroup$
    – JMac
    Jul 26 '17 at 10:22
  • 1
    $\begingroup$ @Krumelur : No. Your calculation assumes the drop in temperature is proportional to time, but this is not true. The temperature drop per hour gets smaller as the temperature difference with the surroundings decreases. If the drop is say 12 degrees in 12 hours it will not be 1 degree in the first hour - it will be more like 4 degrees, then 3, then 2, then 1 etc. So the comparison is between raising the temperature by 4 degrees every hour (= 48 degrees every 12 hours) or by 12 degrees every 12 hours. $\endgroup$ Jul 26 '17 at 10:31

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