# Understanding thermodynamic equilibrium

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• phoenix95
In summary, this conversation provides a starting point for someone studying thermodynamics in equilibrium, as well as references for further reading.
phoenix95
Gold Member
My thermodynamics is rusty and my current endeavors demand me to wield it, so here we go: I need a good starting point and/or references to study physical systems in thermodynamic equilibrium. Any references which address the fluid mechanics perspective of said systems are welcome too. Let me state the problem at hand:

Suppose there are N bodies with temperatures T1, T2, T3..... Tn all are isolated from each other. And at t=0 the isolations are removed and the bodies are allowed to exchange information and reach thermal equilibrium. Then what would be the final temperature of the ensemble? What is the time taken to reach that equilibrium? How would you model the energy and entropy exchange between the bodies?

While framing this question, I noticed something else: you only assign a temperature to a system, if it is in thermodynamic equilibrium. So at t=0, when the isolations are removed, the system as a whole is not in thermal equilibrium (am I correct?). And until this ensemble reaches that equilibrium, it makes no sense to say 'temperature' (is it correct?). If so, how would you characterize a system, which is not in thermal equilibrium? What would you use, in place of 'temperature' to describe the system?

I know the question seems a bit too simplistic and vague. But any answers with a couple of references for further reading will be greatly appreciated.

There are lots of good textbooks on thermodynamics. Considering your question, I think you would be well served by the pedagogical approach of Schroeder's Thermal Physics, or by an old-school text like Callen's Thermodynamics and an Introduction to Thermostatistics. Once the basics have been acquired, application to fluids can be found in a textbook such as W. J. Thomson, Introduction to Transport Phenomena.

phoenix95 said:
Suppose there are N bodies with temperatures T1, T2, T3..... Tn all are isolated from each other. And at t=0 the isolations are removed and the bodies are allowed to exchange information and reach thermal equilibrium. Then what would be the final temperature of the ensemble? What is the time taken to reach that equilibrium? How would you model the energy and entropy exchange between the bodies?
That should be "exchange energy," not "exchange information." The final temperature will depend on the heat capacity of each system. Time taken to reach equilibrium will depend on heat conductivity and the difference in temperature, see https://en.wikipedia.org/wiki/Newton's_law_of_cooling.

The exact way to model this will depend on the systems. For realistic cases, this requires computer simulations.

phoenix95 said:
While framing this question, I noticed something else: you only assign a temperature to a system, if it is in thermodynamic equilibrium. So at t=0, when the isolations are removed, the system as a whole is not in thermal equilibrium (am I correct?).
Correct.
phoenix95 said:
And until this ensemble reaches that equilibrium, it makes no sense to say 'temperature' (is it correct?). If so, how would you characterize a system, which is not in thermal equilibrium? What would you use, in place of 'temperature' to describe the system?
For the entire system, it is characterized by energy. But you can still have local equilibrium and talk of the temperature at a given point. This is done all the time in fluid dynamics. This is how you get something like flame temperature profiles:
https://en.wikipedia.org/wiki/File:Anatomy_of_a_candle_flame.svg

Lord Jestocost and phoenix95
DrClaude said:
That should be "exchange energy," not "exchange information."
When I was thinking of the example above, I thought that the primary means of heat exchange between the said bodies would be through radiation (of course, conduction and convection were possible, but the focus of my study is the radiative heat transfer). And I thought that the photons would carry information (synonymous with entropy), in addition to heat. Could I be wrong in describing so? That is to say, the word 'information' carries no meaning in the context?
DrClaude said:
For the entire system, it is characterized by energy. But you can still have local equilibrium and talk of the temperature at a given point. This is done all the time in fluid dynamics. This is how you get something like flame temperature profiles:
https://en.wikipedia.org/wiki/File:Anatomy_of_a_candle_flame.svg
This was exactly what I was looking for. Do the same references you mentioned above cover this as well? Or are there any others I should take note of?

phoenix95 said:
Could I be wrong in describing so? That is to say, the word 'information' carries no meaning in the context?
I wouldn't use information in this context.

phoenix95 said:
This was exactly what I was looking for. Do the same references you mentioned above cover this as well? Or are there any others I should take note of?
It is covered in Thomson's book. The basics should be found in textbooks on fluid dynamics, such as D. J. Tritton, Physical Fluid Dynamics. Look for "convection."

phoenix95 and Lord Jestocost

## 1. What is thermodynamic equilibrium?

Thermodynamic equilibrium is a state in which a system is at a stable and balanced energy level, with no net exchange of energy or matter occurring within the system or with its surroundings.

## 2. How does a system reach thermodynamic equilibrium?

A system can reach thermodynamic equilibrium through processes such as heat transfer, work, and chemical reactions, which allow the system to reach a state of maximum stability and minimum energy.

## 3. What are the implications of thermodynamic equilibrium?

Thermodynamic equilibrium has important implications in fields such as chemistry, physics, and engineering. It allows us to predict the behavior of systems and understand the direction of energy and matter flow.

## 4. Can thermodynamic equilibrium be maintained indefinitely?

In theory, a system can remain in thermodynamic equilibrium indefinitely as long as there is no external influence or disturbance. However, in reality, most systems are constantly changing and therefore do not remain in equilibrium for long periods of time.

## 5. How is thermodynamic equilibrium different from dynamic equilibrium?

Thermodynamic equilibrium refers to a state of balance in a system with no net energy or matter exchange, while dynamic equilibrium refers to a state of balance in a system where the rates of opposing processes are equal but there is still energy or matter exchange occurring.

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