Heat Transfer Problem Confused

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Discussion Overview

The discussion revolves around a heat transfer problem involving an electrical resistor connected to a battery, focusing on the application of energy balance equations in a steady-state scenario. Participants explore the terms related to energy input, output, generation, and storage within the context of thermal dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to approach the problem and the meaning of various terms in the energy balance equation.
  • Another participant suggests reasoning through each term individually to clarify the situation.
  • Some participants propose that energy input (Ein) may be zero since heat flows from the hotter resistor to the cooler environment, but they are uncertain about the specifics of heat transfer mechanisms (convection, conduction, radiation).
  • There is a discussion about whether Ein and Eout should be treated as separate terms or combined, with some participants expressing dissatisfaction with the problem's wording.
  • Participants mention that the thermal energy generated is likely related to the power output of the battery, but there is uncertainty about how this fits into the energy balance.
  • One participant suggests that the stored energy term may also be zero, as they believe only the generated thermal energy and energy out terms are relevant.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the values of Ein, Eout, Eg, and Est, and there are multiple competing views regarding the interpretation of the energy terms and the assumptions made in the problem.

Contextual Notes

Participants note limitations in the problem's information, particularly regarding the thermal conductivity of the resistor and the assumptions about energy transfers being limited to thermal energy rather than electrical energy.

aisu1
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I'm super confused about this problem. I don't even know where to start. It seems very simple, but I just can't figure it out..

An electrical resistor is connected to a battery. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of 95 degrees C, while the battery and lead wires remain at the ambient temperature of 25 degrees C. Neglect the electrical resistance of the lead wires.

Consider the resistor as a system about which a control surface is placed and the equation Estored=Ein-Eout+Thermal_Egenerated is applied. Determine the corresponding values of Ein (W), Eout (W), Eg (W), and Est (W).

I have a feeling that a lot of these terms cancel out.. but I just don't even know where to start.
 
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Hi aisu1, welcome to PF. Start by reasoning through each term individually. What are your thoughts?
 
Thanks :)

Well, I think that there's in Ein maybe because it's heat and heat goes from higher to lower temperature. So, Eout is q=q''A.. But I don't know if the heat gets transferred via convection, conduction to the outside air, radiation, or through the wires.. And either way, I feel like I'm not given enough information to figure out the thermal conductivity of the resistor.

I think the thermal energy generated is the power generated by the battery.. But that could be the Ein (if Ein isn't 0).
 
aisu1 said:
Well, I think that there's in Ein maybe because it's heat and heat goes from higher to lower temperature.

The resistor is hotter than the surrounding environment. What does that tell you about E_\mathrm{in}?

(Personally, I don't like the way the problem is constructed where E_\mathrm{in} and E_\mathrm{out} are separate terms. There should be one term; if it's positive (negative), then energy is entering (leaving).)

aisu1 said:
And either way, I feel like I'm not given enough information to figure out the thermal conductivity of the resistor.

The thermal conductivity governs temperature changes within an object. The system boundary encloses the entire resistor, so its thermal conductivity is irrelevant.

aisu1 said:
I think the thermal energy generated is the power generated by the battery.. But that could be the Ein (if Ein isn't 0).

Another problem with the wording of this problem is that it seems to be assumed (but not stated) that E_\mathrm{in} and E_\mathrm{out} represent transfers of thermal energy only, not electrical energy. But anyway, I agree that the thermal energy generation term is meant to include the power delivered by the battery.

And what can you say about the stored energy term?
 
The resistor is hotter than the surrounding environment. What does that tell you about Ein?

So, Ein would equal 0, because there is no heat transfer to the resistor, just away from it.

And what can you say about the stored energy term?

I think the stored energy would be 0 also. You only have the generated thermal energy and the energy out terms.
 
Right on!
 
Thanks :) I think it makes much more sense now.
 

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