Why can one calculate entropy change for thermal conduction?

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Discussion Overview

The discussion centers on the calculation of entropy change during thermal conduction between a hot object and a cold object, exploring the conditions under which these calculations can be treated as reversible processes despite the actual irreversible nature of thermal conduction.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that because entropy is a state function, any reversible path connecting the same initial and final states can be used to calculate entropy change.
  • One participant suggests that to determine the entropy change for an irreversible process, one should focus solely on the initial and final states and devise a reversible path between them.
  • Another participant describes a method involving the use of a series of constant temperature reservoirs to gradually and reversibly bring each object to the final temperature, thereby calculating the change in entropy for each object individually.
  • There is a reference to the integral of dq/T as a means to calculate the entropy change along the reversible path.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the reversible paths and the implications of treating the process as reversible. The discussion does not reach a consensus on the best approach or the validity of the proposed methods.

Contextual Notes

Participants note the importance of defining the reversible paths and the assumptions involved in calculating entropy changes, but specific limitations or unresolved issues are not detailed.

Who May Find This Useful

This discussion may be of interest to those studying thermodynamics, particularly in understanding the concepts of entropy, reversible and irreversible processes, and the implications of state functions.

Philip Koeck
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A hot object in thermal contact with a cold one will finally reach a temperature in between. Why can the entropy change of each object be calculated as if the process was reversible? Is there a reversible process with the same final and initial state and what would that be?
 
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Because entropy is a state function, you can use any path joining the same initial and final state. Specifically, you can bring each of the two object reversibly on that temperature on their own.
 
Philip Koeck said:
A hot object in thermal contact with a cold one will finally reach a temperature in between. Why can the entropy change of each object be calculated as if the process was reversible? Is there a reversible process with the same final and initial state and what would that be?
To determine the entropy change for an irreversible process, the first step is to TOTALLY FORGET ABOUT THE ACTUAL IRREVERSIBLE PROCESS THAT BROUGHT THE SYSTEM FROM ITS INITIAL STATE TO THE FINAL STATE, and focus only on the two end states.
Step 2: Devise a reversible path between the two end states. There are an infinite number of reversible paths, and they all give the same result for the entropy change, so anyone will do. Choose one that is simple to apply step 3.
Step 3: Calculate the integral of dq/T for this reversible path.

This is what they mean when they say delta S is the integral of dqrev/T.

In the case of the hot object and the cold object, the final state has a temperature somewhere in-between the initial temperatures of the two. If I were doing Step 2, I would first separate the two objects, and then devise a reversible process to bring each of them to the final state individually. To do this, for each object, I would contact it with a continuous sequence of constant temperature reservoirs, each reservoir having a temperature slightly different from the previous one. Using these reservoirs, I would very gradually and reversibly bring each object to the final temperature that was attained in the irreversible process. In Step 3, I would then calculate the change in entropy of each object individually, and then add the two changes in entropy to get the overall change.
 
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Thank You. That was a very helpful answer.
 

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