The essential principle difference between the microcanonical and canonical Ensemble is that in the former the energy of the system is constant E, while in the latter the energy fluctuates in such a way that the value of the internal energy corresponding to the thermodynamic state of U = (E). the system is the expected value of its energy, Let us now examine this difference in the case of an ideal gas. Let the number of particles in the gas be N, the temperature T and the volume V. Determine the relative rms-value (root-mean-square) of the energy fluctuation for the gas. SErms ___ [[(E – U)²)]¹/² - U U what is the magnitude of the fluctuations with the macroscopic number of particles?
The essential principle difference between the microcanonical and canonical Ensemble is that in the former the energy of the system is constant E, while in the latter the energy fluctuates in such a way that the value of the internal energy corresponding to the thermodynamic state of U = (E). the system is the expected value of its energy, Let us now examine this difference in the case of an ideal gas. Let the number of particles in the gas be N, the temperature T and the volume V. Determine the relative rms-value (root-mean-square) of the energy fluctuation for the gas. SErms ___ [[(E – U)²)]¹/² - U U what is the magnitude of the fluctuations with the macroscopic number of particles?
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![The essential principle difference between the microcanonical and canonical Ensemble is that in
the former the energy of the system is constant E, while in the latter the energy fluctuates in
such a way that the value of the internal energy corresponding to the thermodynamic state of
U = (E)
the system is the expected value of its energy,
Let us now examine this difference in the case of an ideal gas. Let the number of particles in the
gas be N, the temperature T and the volume V. Determine the relative rms-value
(root-mean-square) of the energy fluctuation for the gas.
SErms
U
what is the magnitude of the fluctuations with the macroscopic number of particles?
[((E – U)²)] ¹/²
U](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f1f56f6-a769-4b12-a499-cf1e3f7149ba%2Fec0d0f4c-f4b1-4547-9e54-ed8801a9d391%2Fcqpgrm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The essential principle difference between the microcanonical and canonical Ensemble is that in
the former the energy of the system is constant E, while in the latter the energy fluctuates in
such a way that the value of the internal energy corresponding to the thermodynamic state of
U = (E)
the system is the expected value of its energy,
Let us now examine this difference in the case of an ideal gas. Let the number of particles in the
gas be N, the temperature T and the volume V. Determine the relative rms-value
(root-mean-square) of the energy fluctuation for the gas.
SErms
U
what is the magnitude of the fluctuations with the macroscopic number of particles?
[((E – U)²)] ¹/²
U
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