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I have 20 gallons of water (salt water, but this might be irrelevant). These 20 gallons have a heater that maintains a minimum of 78º F.

With the increasing temperatures during summer, the water during the day can go up to 80ºF. (Gain of 2 aprox).

My question is: If the heater was set to maintain a minimum of 80ºF would the increase in the room temperature affect the 20 gallons in the same way? Would it go up to 82ºF or would it stay the same since the difference with room temperature is less?

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If you are using a good temperature controller it should hold that temperature at the set point almost regardless of external atmospheric temperature. As the external temperature rises it would use less power to maintain the fixed set point. As external temperature fall it will compensate by adding more power to match the heat loss from the tank.

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What is important to understand here is that the system is always going to try to attain equilibrium. So if you're temperature surroundings are the same as before , your tank will still attain the same temperature as it did before. However it is necessary to mention the time taken to reach this temperature or at least whether the temperature varies very very little with the passage of time as the rate of rise in temperature of the water in the tank decreases alot with time. So , assuming that the temperature change is negligibly small with time at 82 degrees , will imply that the surrounding temperature is close to that value and the tank will attain that value(82 degrees). Then , whether you start with water at 80 or 82 degrees shouldn't matter. Infact , if you take water at say 85 degrees , the tank would lose heat to the surroundings to attain 82 degrees.

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According to what I know, if the temperature of the room is increasing that is, heat is being input into the system, the water will gain heat from the air regardless of the temperature difference between the water and the Room. according to the equation H=M x c(Specific Heat capacity) x change in temp. However due to the difference in the final temperatures of the Room and water, heat will move in or out and attempt to balance out the overall temperature of the system. Thus it would all depend on the amount of heat available for the water to gain and finally what difference of temperature exists between the water and room.

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It depends on what kind of heater you are using. If it can hold the temperature on fixed point regardless of other temperature factors, then the temperature will be 80ºF. If not then it will add the power it is fixed to and temperature will rise beyond that.

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