Heating Water: Does Energy Loss Affect Temperature Change?

[charlesworth]

Suppose a constant volume of water is being heated up by a constant amount of power. After some time it is noted that the rate of change of temperature is slowing down. (In this scenario, assume all temperatures to be between 10 and 90 degrees celsius)

What would cause this non-linear relationship between time and temperature?
Q = mc(delta)T --> This does not take into account the masses current temperature.

Does it have to do with energy loss of the substance to outer environment?

 

[Clausius2]

Suppose a constant volume of water is being heated up by a constant amount of power. After some time it is noted that the rate of change of temperature is slowing down. (In this scenario, assume all temperatures to be between 10 and 90 degrees celsius)
What would cause this non-linear relationship between time and temperature?
Q = mc(delta)T --> This does not take into account the masses current temperature.
Does it have to do with energy loss of the substance to outer environment?

1) I don't know what you mean with "masses current temperature"

2) Your equation is only valid for a constant flux of heat in time.

3) You are not taking into account possible heat losts to the environment.

4) In a mathematical model, using ONLY the equation you posted it is impossible a non linear relation between T and Q.

 

[ZapperZ]

Suppose a constant volume of water is being heated up by a constant amount of power. After some time it is noted that the rate of change of temperature is slowing down. (In this scenario, assume all temperatures to be between 10 and 90 degrees celsius)
What would cause this non-linear relationship between time and temperature?
Q = mc(delta)T --> This does not take into account the masses current temperature.
Does it have to do with energy loss of the substance to outer environment?

Yes. The rate of heat loss depends on the temperature gradient. The more you heat the water, the greater the temperature difference between the water and the surrounding air, and thus, the higher the rate of heat loss. Since you are supplying a constant rate of energy to the water, and the water is losing a larger rate of heat as its temperature increases, you will end up with a temperature increase of the water slowing down.

Zz.