Statistical mechanics question

In summary, the conversation discusses a hypothetical situation where more electrons are in the higher energy state than the lower energy state of a two level system, leading to a population inversion. The effective temperature in this situation must be negative. The conversation also explores the effective temperature when populations are swapped and when all electrons are in the upper state. The Boltzmann factor may be relevant in finding a solution.
  • #1
bon
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Homework Statement



Suppose that by some artificial means it is possible to put more electrons in the higher energy state than in the lower energy state of a two level system. Now it is clear that this system cannot be an equilibrium situation, but, nevertheless, for the time that the system is in this strange state we could, if we wished, still express the ratio of the populations in the upper and lower states by some parameter we can think of as an effective temperature.

(i) show that for such a population inversion to exist, the effective temperature must be negative

(ii) imagine that i have electrons that populate the two states in the normal manner at room temperature. I then somehow swap the populations (i/e/ all the ones that were in thw lower temperature go into the upper state, and vice versa) What is the new effective temperature?

(iii) what is the effective temperature if I put all the electrons in the upper state?



Homework Equations





The Attempt at a Solution



Not really even sure where to begin! Any help would be great..thanks! :)
 
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  • #2
any ideas? I am guessing it has something to do with the Boltzmann factor..?
 
  • #3
heloooo
 

1. What is statistical mechanics?

Statistical mechanics is a branch of physics that uses statistical methods to study the behavior of a large number of particles in a system. It aims to explain macroscopic properties of matter, such as temperature and pressure, by understanding the microscopic behavior of individual particles.

2. How does statistical mechanics differ from classical mechanics?

Classical mechanics deals with the motion of individual particles, while statistical mechanics deals with the behavior of a large number of particles in a system. Classical mechanics is deterministic, meaning that the future state of a system can be predicted from its initial conditions, while statistical mechanics is probabilistic, taking into account the random motions of particles.

3. What is the significance of entropy in statistical mechanics?

Entropy is a measure of the disorder or randomness in a system. In statistical mechanics, it is related to the number of possible microstates, or arrangements of particles, in a given macrostate. The second law of thermodynamics states that the total entropy of a closed system always increases, which is a fundamental principle in statistical mechanics.

4. What are the main principles of statistical mechanics?

The main principles of statistical mechanics include the postulate of equal a priori probabilities, which states that all microstates are equally likely to occur, and the principle of maximum entropy, which states that a system will tend towards the state with the highest entropy. These principles, along with the laws of thermodynamics, form the basis of statistical mechanics.

5. How is statistical mechanics applied in other fields?

Statistical mechanics has applications in various fields, including chemistry, biology, and materials science. In chemistry, it is used to study the behavior of molecules in a chemical reaction. In biology, it is used to understand the behavior of proteins and other biomolecules. In materials science, it is used to study the properties of materials at a microscopic level, such as thermal conductivity and phase transitions.

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