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MMLU-Pro / 12131 / The P, v, T relation of a real gas is represented with reasonable accuracy by…

Problem

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

question

The P, v, T relation of a real gas is represented with reasonable accuracy by the relation v = (RT / P) + b - (a / RT) where a and b are constants. For this gas find the change in enthalpy and entropy along an isothermal path between pressures P_1 and P_2.

category

engineering

options

  1. (h_2 - h_1)_T = [b - (2a / RT)] (P_1 - P_2), (s_1 - s_2)_T = Rln(P_2 / P_1) - [{a(P_2 - P_1)} / (RT^2)]
  2. (h_2 - h_1)_T = [b - (3a / RT)] (P_2 - P_1), (s_1 - s_2)_T = - Rln(P_2 / P_1) - [{a(P_2 - P_1)} / (RT^3)]
  3. (h_2 - h_1)_T = [b - (a / RT)] (P_2 - P_1), (s_1 - s_2)_T = Rln(P_2 / P_1) + [{a(P_2 - P_1)} / (RT^2)]
  4. (h_2 - h_1)_T = [b - (2a / RT)] (P_2 - P_1), (s_1 - s_2)_T = - Rln(P_1 / P_2) - [{a(P_1 - P_2)} / (RT^2)]
  5. (h_2 - h_1)_T = [b + (2a / RT)] (P_1 - P_2), (s_1 - s_2)_T = - Rln(P_1 / P_2) + [{a(P_1 - P_2)} / (RT^2)]
  6. (h_2 - h_1)_T = [b - (2a / RT)] (P_1 - P_2), (s_1 - s_2)_T = - Rln(P_1 / P_2) + [{a(P_1 - P_2)} / (RT^2)]
  7. (h_2 - h_1)_T = [b + (2a / RT)] (P_2 - P_1), (s_1 - s_2)_T = - Rln(P_2 / P_1) + [{a(P_2 - P_1)} / (RT^2)]
  8. (h_2 - h_1)_T = [b + (2a / RT)] (P_2 - P_1), (s_1 - s_2)_T = Rln(P_1 / P_2) + [{a(P_1 - P_2)} / (RT^2)]
  9. (h_2 - h_1)_T = [b - (2a / RT)] (P_2 - P_1), (s_1 - s_2)_T = - Rln(P_2 / P_1) - [{a(P_2 - P_1)} / (RT^2)]
  10. (h_2 - h_1)_T = [b + (a / RT)] (P_2 - P_1), (s_1 - s_2)_T = - Rln(P_1 / P_2) - [{a(P_1 - P_2)} / (RT^2)]

src

stemez-Thermodynamics

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Source and history

upstream_id / Original problem ID
12131
task_id
b4a58959-b498-515a-8a91-eefc2e5806cd
task_key
default--test--12131
task_revision_id
1
config / split
default / test

Official source

initial import