Suppose a water tank with a depth of one meter with a water temperature of 12 °C is placed in a closed hall with an air temperature of 32 °C. The dimensions of the tank are 10 x 4 meters and the volume is 40 cubic meters. How long does it take for the temperature of the pool water to be the same as the air temperature of the hall (=32)?
The decrease in air temperature in the hall is compensated by the heater and is always constant at around 32 degrees.
As the heat transfer to the water is an asymptotic process, the temperature will never be the same. It will take an infinite amount of time. :-)
In the following, the appropriate answer of Dr. Ingo Riess
The temperature of the air in gaseous conditions and the temperature of the water environment are never equal due to the different process components. But they can influence each other to reach a relative balance.
I agree with my colleagues. The water temperature in the tank never reaches the air temperature in the hall. For that, additional energy would be needed. Over a period of time, the water and air temperatures will equalize, as long as no energy wil be supplied to either environment (water and air, respectively).
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