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In a classical microcanonical ensemble for a system of N interacting particles, the fundamental volume in phase space which is regarded as equivalent to one microstate is.
Select one:
Select one:
- a)h3N
- b)hN
- c)h
- d)h2N
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a classical microcanonical ensemble for a system of N interacting p...
For the particle, volume of phase space corresponding to one microstate is
dV = (dxdydz)(dpxdpydpz)
= h3
For N interacting particles, the volume of one microstate is
= (h3)·h3 ···N terms
The correct answer is: h3N
dV = (dxdydz)(dpxdpydpz)
= h3
For N interacting particles, the volume of one microstate is
= (h3)·h3 ···N terms
The correct answer is: h3N
Most Upvoted Answer
In a classical microcanonical ensemble for a system of N interacting p...
Fundamental volume in phase space
In the microcanonical ensemble, the system is considered to be isolated and is characterized by a fixed total energy, volume, and number of particles. Each possible state of the system is represented by a point in a high-dimensional space called phase space. The volume occupied by all possible states of the system is known as the fundamental volume in phase space.
Equivalence of microstates
The concept of microstates refers to the different ways in which the system can distribute its energy among its particles while satisfying the given constraints. In the classical microcanonical ensemble, all microstates with the same total energy, volume, and number of particles are considered equally probable.
Derivation of the answer
To find the fundamental volume in phase space equivalent to one microstate, we need to consider the number of possible momentum states and position states for each particle in the system.
- Each particle in the system can have its momentum specified by three independent variables (px, py, pz) due to the three-dimensional nature of space.
- Each particle can also have its position specified by three independent variables (x, y, z) due to the three-dimensional nature of space.
Therefore, the phase space volume for each particle is given by h^3, where h is the Planck's constant divided by 2π.
Since we have N particles in the system, the total phase space volume for all particles is given by (h^3)^N = h^(3N).
Conclusion
In the classical microcanonical ensemble for a system of N interacting particles, the fundamental volume in phase space equivalent to one microstate is h^3N. This means that each microstate of the system occupies a volume of h^3N in phase space.
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