About Ensemble Average for gas molecules(classical mechanics regime)

In summary, the conversation discusses the concept of ensemble average and its relation to macroscopic and microscopic variables in fluid dynamics. The speaker also raises a question about whether two different microscopic variables with the same average value can be considered the same state from a macroscopic perspective. The responder provides an explanation of how this concept fits into thermodynamics and its implications for entropy.
  • #1
Noh-hoon Lee
8
0
I have some question about Ensemble Average.

The macroscopic variable of fluid is average of microscopic variable of gas molecule.

And if time average is same with spatial average I know as it called edgodic.

My question is that if two different microscopic variables which have same average value, like center of mass, momentum, translational energy, (angular momentum has some error but it is very small so I ignore it.(it is acceptable error))

Does it can be seen as a same state for macroscopic view?
 
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  • #2
Every microstate is unique configuration of particle states and. In pursuit of thermodynamics, we say that there are many different microstates for the same macrostate, so long as they have the same ensemble averages. The number of microstates for a given macrostate determines its entropy, and from there, all the rest of thermodynamics can follow.


Noh-hoon Lee said:
I have some question about Ensemble Average.

The macroscopic variable of fluid is average of microscopic variable of gas molecule.

And if time average is same with spatial average I know as it called edgodic.

My question is that if two different microscopic variables which have same average value, like center of mass, momentum, translational energy, (angular momentum has some error but it is very small so I ignore it.(it is acceptable error))

Does it can be seen as a same state for macroscopic view?
 
  • #3
thank you for your reply :) It's really helpful
 

1. What is the definition of ensemble average for gas molecules in the classical mechanics regime?

The ensemble average for gas molecules in the classical mechanics regime is the average value of a physical property of a gas molecule, such as its velocity or position, over a large number of molecules in a system. It is a statistical concept that takes into account the behavior of all molecules in the system, rather than focusing on individual molecules.

2. How is the ensemble average calculated for gas molecules in the classical mechanics regime?

The ensemble average for gas molecules in the classical mechanics regime is calculated by taking the sum of the values of the physical property for each molecule in the system, and dividing it by the total number of molecules in the system. This provides an overall average value for the property in question.

3. Why is the concept of ensemble average important in classical mechanics?

In classical mechanics, the behavior of individual molecules is difficult to predict and can be highly variable. The concept of ensemble average allows us to understand and describe the behavior of a system of molecules as a whole, providing a more accurate and useful description of the system.

4. What is the difference between ensemble average and time average in classical mechanics?

Ensemble average takes into account the behavior of all molecules in a system at a given time, whereas time average focuses on the behavior of a single molecule over a period of time. Ensemble average provides a more comprehensive understanding of the system, while time average allows for a more detailed analysis of the behavior of individual molecules.

5. How does the concept of ensemble average relate to the kinetic theory of gases?

The kinetic theory of gases is based on the assumption that the behavior of a gas can be described by the average behavior of its molecules. This is essentially the concept of ensemble average, where the properties of a gas are described by the average behavior of all its molecules, rather than individual molecules. Therefore, the concept of ensemble average is closely related to the kinetic theory of gases.

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