Calculating Entropy Change of a Wire Conduction

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Homework Help Overview

The discussion revolves around calculating the total change in entropy for a metal wire that is in thermal contact with two heat reservoirs at different temperatures. The problem involves understanding the heat transfer process and its implications on entropy change.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore which temperature to use in the entropy formula, questioning whether to average the temperatures or use one specific temperature. There is also a discussion about the need to consider the entropy changes of both reservoirs separately.

Discussion Status

Some participants have provided guidance on how to approach the problem by suggesting the calculation of entropy changes for each reservoir individually and then summing them. There is an acknowledgment of the need to be careful with the signs of the entropy changes based on the direction of heat flow.

Contextual Notes

Participants note that the entropy change of the wire itself can be ignored, focusing instead on the heat transfer between the reservoirs. The discussion also touches on the assumption that the temperatures of the reservoirs remain constant during the heat transfer process.

pizzafihop
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Homework Statement


Each end of a metal wire is in thermal contact with a different heat reservoir. Reservoir 1 is at a temperature of 752 K, and reservoir 2 is at a temperature of 345 K. Compute the total change in entropy that occurs from the condustion of 1096 J of heat through the wire.

Homework Equations


dS = dQ / T

The Attempt at a Solution


Which T should I use? Should I average them? Use only one? Divide one by the other?
 
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pizzafihop said:

Homework Statement


Each end of a metal wire is in thermal contact with a different heat reservoir. Reservoir 1 is at a temperature of 752 K, and reservoir 2 is at a temperature of 345 K. Compute the total change in entropy that occurs from the condustion of 1096 J of heat through the wire.

Homework Equations


dS = dQ / T

The Attempt at a Solution


Which T should I use? Should I average them? Use only one? Divide one by the other?
First of all, you have to ignore the entropy change of the wire. Then it is just a matter of heat flowing out of the hot reservoir and heat flowing into the cold reservoir without changing the temperature of either. Calculate the entropy change of the hot reservoir. Calculate the entropy change of the cold reservoir. Add them together (be careful of the signs - flow into is positive/flow out is negative).

AM
 
Thanks, I didn't realize I had to split the formula in 2 for each reservoir.
 
pizzafihop said:
Thanks, I didn't realize I had to split the formula in 2 for each reservoir.
To calculate the total entropy change you have to sum the entropy changes of the parts.

Generally, you would divide the entire system into infinitessimal slices and do an integral of the heat flows/surface temperature into and out of each slice. In this case there is no temperature gradient within the reservoir so you can look at the reservoir as a whole. All the heat leaves or enters the reservoir at the same temperature. So just determine the entropy change for each reservoir and add them together to get the total entropy change for the system.

Once the wire heats up there is a stable temperature gradient along the wire so its thermodynamic state does not change. You are then left with only the entropy changes in each reservoir.

AM
 

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