How to calculate the power to heat 3000 liters of water?

I am planning to build a hydrographic reservoir. I plan to build a bathtub with dimensions of 2x1.5x1 meters. The water temperature in the tank must be 30 degrees, suppose now the starting water temperature now in the coldest period is about 5 degrees. So you need to heat the water by about 25 degrees within, say, an hour. The water circulation will be forced by the pump. What kind of heater is needed to heat this amount in an hour?

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To heat 1l of water by 1 ° C, you need to supply 4200J of energy, so:
4200J * 3000l * 25 ° C = 315MJ = 87.5 kWh
Adding efficiency and losses, a 100kW heater is needed to heat the water in an hour.

temperature increase = 25 K, water mass = 3000 kg, specific heat of water approx. 4.2 kJ / kg * K.
It takes 25 x 3,000 x 4.2 = 315,000 kJ = 87.5 kWh for heating
that is, to heat 3 m3 of water in one hour, you need a 87.5 kW heater. A large heater :)

12pawel wrote:

Adding efficiency and losses, a 100kW heater is needed to heat the water in an hour.

The efficiency of the heater immersed in water is 100%, losses when heating up to 30 degrees can practically be neglected (I assume that the tank is in a heated room and not outside) and the bathtub is unlikely to be filled to the overflow, i.e. the water will be about 10% less than we assumed in calculations.

Let us assume theoretically that I would have such a heater and the appropriate connection power. Is it possible to somehow determine what would be the heat loss of water temperature after 15 hours of non-heating? I finish work and go home, turn off the heater and what temperature will I find in the morning? Suppose the tank was insulated with 10cm of Styrofoam. Can it be calculated at all? However, would it be a better solution to install a thermostat so that the heater turns on automatically? What would it cost to keep it at 30 degrees non-stop?

The old ones will be the biggest by the surface - it would have to be covered.

How's the ambient temperature? what is the temperature difference because the losses will depend on it

If it is to be continuous work - several hours a day from Monday to Friday, you can apply the following solution; turning on the heater (clock) on Monday, e.g. 4 hours before starting work (20-25 kW is then enough)
3-5 kW at a room temperature of 20 degrees should be sufficient to maintain the temperature. at this temperature, even 5 cm of polystyrene is enough to insulate the sides. It all depends as a colleague wrote Dacomos from the ambient temperature. One or two layers of bubble wrap can be used to cover the surface.

vodiczka wrote:

3-5 kW should be sufficient to maintain the temperature

It should also be taken into account that the elements immersed in the bath will probably have a lower temperature and will additionally cool the liquid.

Of course, but it depends on the size of the elements and the heat capacity of the material they are made of. The ambient temperature bows again, if the elements are stored at 20 degrees and made of plastic, they will absorb little heat.
Maybe the author of the topic will tell you what temperature he will keep in the room.
I think that there is no need for a thermostat.

But gentlemen, 2x1.5x1 m = 3 m? and this does not equal 3,000 but 30,000 liters.
So I break all my calculations.

As for the efficiency - the heater is 100% as possible, but you can never isolate the boiler perfectly, so you have to assume some losses (efficiency) for the boiler.

12pawel - you calculated it nicely, but why did you assume that it needs to be heated within an hour, and now 1MW HEATER is needed for 30,000 liters - attention Kozienice can sit down.

Aleksander_01 wrote:

But gentlemen, 2x1.5x1 m = 3 m? and this does not equal 3,000 but 30,000 liters.

But buddy, one thing is a small thing, but it's a shame not to know that 1 m3 = 1000 l

vodiczka wrote:

Aleksander_01 wrote:

But gentlemen, 2x1.5x1 m = 3 m? and this does not equal 3,000 but 30,000 liters.

But buddy, a small thing, it's a shame not to know that 1 m3 = 1000 l

Oh, I'm sorry - shame if I don't know what. 10x10x10 = 1000 thousand.
Sorry for the confusion.

I guess it resulted from the fact that during such conversations people often take 100 liters for m?.

I used to work in a large printing house, that's where they used such bathtubs. When buying newer machines, they sold the old ones (and everything was there - heaters, automatics).

When I come to the hall in the morning, now it will be around 8-10 degrees, when it was frosty, it was around 4 degrees in the morning. After about an hour of heating, I have 15 degrees in the hall, then I turn off the gas heaters and heat only with electric heaters and the temperature is slowly rising. It will be plastics such as plastic or laminate. However, I think that it will be more profitable to build two bathtubs, one smaller with a capacity of about 600 liters for smaller elements and one larger. This will probably be the most sensible solution. I have access to cheap construction material. I guess it will be the smartest thing. I think that this small bathtub will be used much more than the big one anyway.
And in the spring I will think about solar panel from a garden hose and put it on the roof.

zadek07 wrote:

... then I turn off the gas heaters and heat only with electric heaters.

If there is access to gas, why such profligacy on heating water with electricity?

Except that it is a cylinder gas. Also, if it would be cheaper and faster, I am asking for suggestions. I would like to point out that there is a fairly tight room with an area of 50 m2, so I would not like the gas to burn for too long.

Aleksander_01 wrote:

12pawel - you figured it out nicely, but why did you assume that you have to heat it up within an hour

I just read with understanding, that's why I assumed so.

zadek07 wrote:

What kind of heater is needed to heat this amount in an hour?

As for heating, I think maintaining the temperature overnight will be less expensive than heating in the morning from scratch.

12pawel wrote:

As for heating, I think maintaining the temperature overnight will be less expensive than heating in the morning from scratch.

I don't think so. The highest heat losses are with the highest temperature difference between the water and the environment. As the water cools, the amount of heat given off per unit time decreases, as opposed to keeping the temperature constant. Therefore, it is recommended, for example, to set the heating of the house so that when leaving for work, the temperature of the rooms is reduced and warmed up before returning.
When the temperature in the hall drops to 6-8 degrees, it may be advisable to use an even thicker insulation layer than assumed by the author and a thermally insulated cover.

A simple experiment - fill the bottle with water at 30 degrees, put it in a suitable polystyrene box and put it in a room at a temperature of 6-8 degrees, measure the water temperature after 5, 10 and 15 hours.

A convenient calculator for calculating the heating time depending on the temperature, heater power and the amount of water:
https://padew.pl/pub/kalkulatormocy.php