What's the relationship between electric power and heat?

[Guidestone]

Hey fellas! Nice to be here again [emoji5]️
Here is the thing, everybody at school keeps telling me that the more power consumed by an electrical component such as a resistor or even a coil the hotter it will get. However, even though I understand that power is energy per unit of time and heat is a form of energy, I just can't see the link between both concepts, at least mathematically. I can just understand it intuitively.

Any answer will be really appreciated!

 

[anorlunda]

Energy can be converted one form to another. Electric power is generated using mechanical power, wind, solar, hydro, nuclear, heat, and chemical energy. Electric can be converted to mechanical (a motor), light, heat (a stove), and so on. That is what makes it so darn useful.

 

[donpacino]

Hey fellas! Nice to be here again [emoji5]️
Here is the thing, everybody at school keeps telling me that the more power consumed by an electrical component such as a resistor or even a coil the hotter it will get. However, even though I understand that power is energy per unit of time and heat is a form of energy, I just can't see the link between both concepts, at least mathematically. I can just understand it intuitively.

Any answer will be really appreciated!

you're referring to instantaneous power.

If you dissipate 50 watts in a component for 1 second, how much energy was dissipated?

 

[reson8r]

Power converted to heat in a component is always dissipated in an effective resistance in the component, so you can use P = I²R or V²/R to determine the power in watts from the current I through the resistance or the voltage V across it.

A resistor is mostly resistance (duh), but real inductors and capacitors have tiny effective resistances in series with their (non-dissipative) inductance or capacitance. Current through those effective resistances leads to power dissipation in those "non-dissipative" components.

Is that the mathematical link you were looking for?

 

[Guidestone]

you're referring to instantaneous power.

If you dissipate 50 watts in a component for 1 second, how much energy was dissipated?

50 Joules I guess. But how's that going to tell me how hot it is? There's something I read a few months ago about the Joule effect. Does it have anything to do in here?

 

[Guidestone]

Power converted to heat in a component is always dissipated in an effective resistance in the component, so you can use P = I²R or V²/R to determine the power in watts from the current I through the resistance or the voltage V across it.

A resistor is mostly resistance (duh), but real inductors and capacitors have tiny effective resistances in series with their (non-dissipative) inductance or capacitance. Current through those effective resistances leads to power dissipation in those "non-dissipative" components.

Is that the mathematical link you were looking for?

I know those equations. They just don't tell me much about heat.
Thank you for the reply :)

 

[donpacino]

look up what a calorie is.

lets assume the the resistive element i discussed is touching exactly 1 gram of water evenly.
how much heat generated in the water.

 

[reson8r]

I think "specific heat" might be more useful -- it's a measure of the amount of energy required to raise a substance a certain number of degrees. With power & time (energy) and specific heat you can determine how hot your object will get dissipating that power.

For example, your real-world inductor is made of a substance with an average specific heat. If you know the current through it and its equivalent resistance you can calculate the power dissipated, and with that + time + specific heat you can determine how hot it will get.

Are we getting closer to the mathematical link you seek?

 

[sophiecentaur]

I think "specific heat" might be more useful

Heat Capacity is also a useful quantity. That looks at a specific object and asks how many Joules are needed to raise its temperature by 1°C. It's just the Specific Heat Capacity times the mass for a lump of a single subsatnce but, for an object with a mix of materials in it, it can be a useful parameter to use.

 

[meBigGuy]

Only if a component dissipates its power as heat, will it will get hotter. If it dissipated it all as light, it would not get hotter. (of course, a real device would not be 100% efficient producing light and some power would be lost as heat, but let's ignore that)

If you had a 100% efficient motor driving a load, then it would consume power and transfer it all to the load. It would not get hotter. The nature of the load would determine whether the load got hotter. (maybe it is lifting a load)

Regarding the conversion of power to temperature:

Electronic components have thermal conductivity to the surrounding environment. It can be expressed in degrees/watt. So if a component dissipates 1 watt as heat and its thermal conductivity to free air is 100C/watt, then it will rise in temperature to 100C. If you connected a heat sink and the conductivity becane 25C/watt, then it would only rise 25C. Forced air could lower it even more, and so on.

 

[sophiecentaur]

some power would be lost as heat,

Oh boy. And that is another can of worms. The basics of 'energy in = X times temperature rise' are never going to apply in reality. There are other forms of internal energy and there is always energy loss to the surroundings.