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MMLU-Pro / 11296 / Calculate the roost probable distribution and the thermodynamicprobability…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Calculate the roost probable distribution and the thermodynamicprobability (\Omega) for a system of eight moleculesdistributed among six available energy levels. The totalsystem energy is 4 ergs and the individual levels have energiesof 0, 1, 2, 3, 4, and 5 ergs, respectfully. Also determinethe entropy of the system.

category

engineering

options

  1. most probable distribution is number 3; \Omega = 250; entropy of the system is 1.82 × 10^-16eu
  2. most probable distribution is number 2; \Omega = 400; entropy of the system is 2.02 × 10^-16eu
  3. most probable distribution is number 1; \(\Omega = 260\); entropy of the system is \(1.75 \times 10^{-16}\)eu
  4. most probable distribution is number 5; \(\Omega = 360\); entropy of the system is \(1.97 \times 10^{-16}\)eu
  5. most probable distribution is number 3; \(\Omega = 290\); entropy of the system is \(1.78 \times 10^{-16}\)eu
  6. most probable distribution is number 1; \Omega = 280; entropy of the system is 1.72 × 10^-16eu
  7. most probable distribution is number 6; \(\Omega = 340\); entropy of the system is \(1.93 \times 10^{-16}\)eu
  8. most probable distribution is number 5; \(\Omega = 310\); entropy of the system is \(1.88 \times 10^{-16}\)eu
  9. most probable distribution is number 4; \Omega = 330; entropy of the system is 1.92 × 10^-16eu
  10. most probable distribution is number 2; \(\Omega = 420\); entropy of the system is \(2.08 \times 10^{-16}\)eu

src

stemez-Thermodynamics

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Source and history

upstream_id / Original problem ID
11296
task_id
3c99d5d5-f4f5-5da7-aba3-2525ca05c760
task_key
default--test--11296
task_revision_id
1
config / split
default / test

Official source

initial import