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MMLU-Pro / 12138 / Determine the equation of state for a certain hypothetical gas whose thermal…

Problem

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

question

Determine the equation of state for a certain hypothetical gas whose thermal coefficient of expansion is \alpha = (1 / V)(\partialV / \partialT)_P = k_1(C_P / C_V)T^{(C)P/(C)V}-1 and the coefficient of isothermal compressibility is \beta = - (1 / V)(\partialV / \partialT)_P = (k_2 / P). In this problem, assume that C_P, C_V, k_1 and k_2 are constants.

category

engineering

options

  1. P^(k)1V = k [T^{(C)P/(C)V} + k_1]
  2. P^(k)2V = k [T^{(C)V/(C)P} + k_2]
  3. PV = k exp [k_1 T^{(C)P/(C)V} + k_2]
  4. P^(k)1V = k exp [k_1 T^{(C)P/(C)V}]
  5. PV^(k)2 = k exp [k_1 T^{(C)V/(C)P}]
  6. P^(k)2V = k exp [k_2 T^{(C)P/(C)V}]
  7. PV = k exp [k_2 T^{(C)P/(C)V - 1}]
  8. P^(k)1V = k exp [k_2 T^{(C)V/(C)P}]
  9. P^(k)2V = k exp [k_1 T^{(C)P/(C)V}]

src

stemez-Thermodynamics

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Source and history

upstream_id / Original problem ID
12138
task_id
d13224fa-d110-528c-8a3c-eff28f2a6071
task_key
default--test--12138
task_revision_id
1
config / split
default / test

Official source

initial import