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MMLU-Pro / 4271 / Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25…

Problem

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question

Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The constant-volume heat capacity of a gas can be measured by observing the decrease in temperature when it expands adiabatically and reversibly. If the decrease in pressure is also measured, we can use it to infer the value of γ=Cp/CV\gamma=C_p / C_V and hence, by combining the two values, deduce the constant-pressure heat capacity. A fluorocarbon gas was allowed to expand reversibly and adiabatically to twice its volume; as a result, the temperature fell from $298.15 \mathrm{~K}$ to $248.44 \mathrm{~K}$ and its pressure fell from 202.94kPa202.94 \mathrm{kPa} to 81.840kPa81.840 \mathrm{kPa}. Evaluate CpC_p.
Plain-text mathematical notation (without MathML)
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The constant-volume heat capacity of a gas can be measured by observing the decrease in temperature when it expands adiabatically and reversibly. If the decrease in pressure is also measured, we can use it to infer the value of γ=C_(p)/C_(V) and hence, by combining the two values, deduce the constant-pressure heat capacity. A fluorocarbon gas was allowed to expand reversibly and adiabatically to twice its volume; as a result, the temperature fell from $298.15 \mathrm{~K}$ to $248.44 \mathrm{~K}$ and its pressure fell from 202.94kPa to 81.840kPa. Evaluate C_(p).
Original LaTeX notation
Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The constant-volume heat capacity of a gas can be measured by observing the decrease in temperature when it expands adiabatically and reversibly. If the decrease in pressure is also measured, we can use it to infer the value of $\gamma=C_p / C_V$ and hence, by combining the two values, deduce the constant-pressure heat capacity. A fluorocarbon gas was allowed to expand reversibly and adiabatically to twice its volume; as a result, the temperature fell from $298.15 \mathrm{~K}$ to $248.44 \mathrm{~K}$ and its pressure fell from $202.94 \mathrm{kPa}$ to $81.840 \mathrm{kPa}$. Evaluate $C_p$.

category

chemistry

options

  1. 29.80$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  2. 47.80$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  3. 38.70$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  4. 44.20$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  5. 55.00$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  6. 33.60$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  7. 41.40$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  8. 50.60$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  9. 35.20$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
  10. 62.50$\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$

src

scibench-atkins

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Source and history

upstream_id / Original problem ID
4271
task_id
9414c161-8a90-5060-8722-0f83e6eaacf7
task_key
default--test--4271
task_revision_id
1
config / split
default / test

Official source

initial import