Heat Transfer Problem Confused

[aisu1]

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 E_stored=E_in-E_out+Thermal_E_generated is applied. Determine the corresponding values of E_in (W), E_out (W), E_g (W), and E_st (W).

I have a feeling that a lot of these terms cancel out.. but I just don't even know where to start.

 

[Mapes]

Hi aisu1, welcome to PF. Start by reasoning through each term individually. What are your thoughts?

 

[aisu1]

Thanks :)

Well, I think that there's in E_in maybe because it's heat and heat goes from higher to lower temperature. So, E_out 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 E_in (if E_in isn't 0).

 

[Mapes]

Well, I think that there's in E_in 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).)

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.

I think the thermal energy generated is the power generated by the battery.. But that could be the E_in (if E_in 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?

 

[aisu1]

The resistor is hotter than the surrounding environment. What does that tell you about E_in?

So, E_in 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.

 

[Mapes]

Right on!

 

[aisu1]

Thanks :) I think it makes much more sense now.