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In relation to statistical mechanics choose the correct statements.
Select one or more:
Select one or more:
- a)All particles of given kind are treated as mutually indistinguishable.
- b)The phase space for n degrees of freedom will have 2n dimensions and it unit cell volume in nn .
- c)Photons may be treated as having fermi-Dirac statistics.
- d)None of the above
Correct answer is option 'A,B'. Can you explain this answer?
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Verified Answer
In relation to statistical mechanics choose the correct statements.Sel...
For a given kind, all particles are exactly the same and are thus indistinguishable.
For each degree of freedom, there is one position coordinate and one canonical momentum,
∴ for n degrees, 2n will be the dimension.
Photons follow Bose Einstein statistics.
The correct answers are: All particles of given kind are treated as mutually indistinguishable., The phase space for n degrees of freedom will have 2n dimensions and it unit cell volume in nn.
For each degree of freedom, there is one position coordinate and one canonical momentum,
∴ for n degrees, 2n will be the dimension.
Photons follow Bose Einstein statistics.
The correct answers are: All particles of given kind are treated as mutually indistinguishable., The phase space for n degrees of freedom will have 2n dimensions and it unit cell volume in nn.
Most Upvoted Answer
In relation to statistical mechanics choose the correct statements.Sel...
The Correct Statements in Relation to Statistical Mechanics:
1. All particles of a given kind are treated as mutually indistinguishable.
In statistical mechanics, particles are typically treated as indistinguishable. This means that the properties of individual particles of the same kind, such as mass or charge, do not affect the overall behavior of the system. The focus is on the statistical distribution of these particles rather than their individual properties. This assumption allows for the use of mathematical tools such as the Boltzmann distribution or the partition function to describe the system.
2. The phase space for n degrees of freedom will have 2n dimensions and its unit cell volume is nn.
The phase space of a system refers to the set of all possible states that the system can occupy. In classical mechanics, the phase space is described by the positions and momenta of all particles in the system. For a system with n degrees of freedom, the phase space will have 2n dimensions. Each dimension corresponds to one degree of freedom.
The unit cell volume in the phase space is given by nn, where n is the number of particles. This means that the volume of each cell in the phase space is proportional to the number of particles raised to the power of the number of degrees of freedom. This result is derived from the assumption of indistinguishability and is a fundamental result in statistical mechanics.
3. Photons may be treated as having Fermi-Dirac statistics.
Photons are bosons, which means they follow Bose-Einstein statistics rather than Fermi-Dirac statistics. Fermi-Dirac statistics apply to particles with half-integer spin, such as electrons, while Bose-Einstein statistics apply to particles with integer spin, such as photons. The distinction between these statistics is important in understanding the behavior of particles at low temperatures, particularly in systems where quantum effects dominate.
Conclusion
In conclusion, the correct statements in relation to statistical mechanics are:
- All particles of a given kind are treated as mutually indistinguishable.
- The phase space for n degrees of freedom will have 2n dimensions, and its unit cell volume is nn.
These statements are fundamental principles in statistical mechanics and are used to describe the behavior of systems with large numbers of particles. The assumption of indistinguishability allows for the use of statistical methods, while the phase space concept provides a framework for understanding the distribution of particle states.
1. All particles of a given kind are treated as mutually indistinguishable.
In statistical mechanics, particles are typically treated as indistinguishable. This means that the properties of individual particles of the same kind, such as mass or charge, do not affect the overall behavior of the system. The focus is on the statistical distribution of these particles rather than their individual properties. This assumption allows for the use of mathematical tools such as the Boltzmann distribution or the partition function to describe the system.
2. The phase space for n degrees of freedom will have 2n dimensions and its unit cell volume is nn.
The phase space of a system refers to the set of all possible states that the system can occupy. In classical mechanics, the phase space is described by the positions and momenta of all particles in the system. For a system with n degrees of freedom, the phase space will have 2n dimensions. Each dimension corresponds to one degree of freedom.
The unit cell volume in the phase space is given by nn, where n is the number of particles. This means that the volume of each cell in the phase space is proportional to the number of particles raised to the power of the number of degrees of freedom. This result is derived from the assumption of indistinguishability and is a fundamental result in statistical mechanics.
3. Photons may be treated as having Fermi-Dirac statistics.
Photons are bosons, which means they follow Bose-Einstein statistics rather than Fermi-Dirac statistics. Fermi-Dirac statistics apply to particles with half-integer spin, such as electrons, while Bose-Einstein statistics apply to particles with integer spin, such as photons. The distinction between these statistics is important in understanding the behavior of particles at low temperatures, particularly in systems where quantum effects dominate.
Conclusion
In conclusion, the correct statements in relation to statistical mechanics are:
- All particles of a given kind are treated as mutually indistinguishable.
- The phase space for n degrees of freedom will have 2n dimensions, and its unit cell volume is nn.
These statements are fundamental principles in statistical mechanics and are used to describe the behavior of systems with large numbers of particles. The assumption of indistinguishability allows for the use of statistical methods, while the phase space concept provides a framework for understanding the distribution of particle states.
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In relation to statistical mechanics choose the correct statements.Select one or more:a)All particles of given kind are treated as mutually indistinguishable.b)The phase space for n degrees of freedom will have 2n dimensions and it unit cell volume in nn .c)Photons may be treated as having fermi-Dirac statistics.d)None of the aboveCorrect answer is option 'A,B'. Can you explain this answer?
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