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MMLU-Pro / 9613 / Consider a system of N particles each of which can exist in only two energy…

Problem

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

question

Consider a system of N particles each of which can exist in only two energy levels + \epsilon and - \epsilon. If the probability of occupying an energy level at temperature T is given by P_E = e- E/KT where E is the energy of the level, and K is Boltzmann's constant, calculate the internal energy of the system.

category

physics

options

  1. -2N\epsilon\cosh(\epsilon/KT)
  2. 2N\epsilon\sinh(\epsilon/KT)
  3. -\epsilonNtanh(\epsilon/KT)
  4. -\epsilonN
  5. N\epsilon^2/KT
  6. 0
  7. \epsilonN(1 - e^{-\epsilon/KT})
  8. \epsilonNtanh(\epsilon/KT)
  9. \epsilonNcoth(\epsilon/KT)
  10. N\epsilon(1 - 2e^{-2\epsilon/KT})

src

stemez-Physics

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Source and history

upstream_id / Original problem ID
9613
task_id
939e7c7f-6e66-56cd-bf77-29669bc66bc7
task_key
default--test--9613
task_revision_id
1
config / split
default / test

Official source

initial import