- #1
FissionChips
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Hi PF,
I've got a very trivial conceptual question regarding the conservation of energy with respect to thermodynamics and heat transfer that I can't seem to figure out.
Suppose I have an electric heating element with a 240 volt, 30 amp supply, in contact with a solid volume of an arbitrary material. P = I*V, so the element will supply a total of 7200 W. Since electric elements are 100% efficient, I can safely say that 7200 W of heat energy will be emitted from the element.
It is my understanding, (perhaps incorrect) that while the element will emit 7200 W indefinitely, and at a constant rate (assuming the voltage and current of the supply does not change), the rate at which this heat energy is received by the solid body is not constant, and is a function of the temperature differential between it and the element surface. So, if the element surface is at 800 K, the temperature of the solid body will approach 800 K logarithmically, and the heat transfer rate between the element and the solid body will become infinitely small as time progresses.
This is where I'm hung up. Assuming I'm still running my element, I'm emitting a constant 7200 W, but as time progresses, only an infinitely small fraction of this is being picked up by the solid body. If this was not the case, the solid body would continue to heat up indefinitely as 7200 Joules of heat energy were pumped into it every second.
I understand that in reality, there are losses of all kinds that account for the difference in energy emitted versus received. However, if we are to assume theoretically ideal conditions (heat transfer is only occurring between the element and the solid body, and there are no losses), where is the balance of energy going?I apologize for having to ask something so simple; I obviously misunderstand the fundamentals of heat transfer.
Thanks!
I've got a very trivial conceptual question regarding the conservation of energy with respect to thermodynamics and heat transfer that I can't seem to figure out.
Suppose I have an electric heating element with a 240 volt, 30 amp supply, in contact with a solid volume of an arbitrary material. P = I*V, so the element will supply a total of 7200 W. Since electric elements are 100% efficient, I can safely say that 7200 W of heat energy will be emitted from the element.
It is my understanding, (perhaps incorrect) that while the element will emit 7200 W indefinitely, and at a constant rate (assuming the voltage and current of the supply does not change), the rate at which this heat energy is received by the solid body is not constant, and is a function of the temperature differential between it and the element surface. So, if the element surface is at 800 K, the temperature of the solid body will approach 800 K logarithmically, and the heat transfer rate between the element and the solid body will become infinitely small as time progresses.
This is where I'm hung up. Assuming I'm still running my element, I'm emitting a constant 7200 W, but as time progresses, only an infinitely small fraction of this is being picked up by the solid body. If this was not the case, the solid body would continue to heat up indefinitely as 7200 Joules of heat energy were pumped into it every second.
I understand that in reality, there are losses of all kinds that account for the difference in energy emitted versus received. However, if we are to assume theoretically ideal conditions (heat transfer is only occurring between the element and the solid body, and there are no losses), where is the balance of energy going?I apologize for having to ask something so simple; I obviously misunderstand the fundamentals of heat transfer.
Thanks!