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MMLU-Pro / 10009 / The mean solar flux at Earth's surface is sim 2.00 mathrm{~J}…

Problem

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

question

The mean solar flux at Earth's surface is $\sim 2.00 \mathrm{~J}$ $\mathrm{cm}^{-2} \mathrm{~min}^{-1}$. In a nonfocusing solar collector, the temperature reaches a value of 79.5∘C79.5^{\circ} \mathrm{C}. A heat engine is operated using the collector as the hot reservoir and a cold reservoir at $298 \mathrm{~K}$. Calculate the area of the collector needed to produce 1000. W. Assume that the engine operates at the maximum Carnot efficiency.
Plain-text mathematical notation (without MathML)
The mean solar flux at Earth's surface is $\sim 2.00 \mathrm{~J}$ $\mathrm{cm}^{-2} \mathrm{~min}^{-1}$. In a nonfocusing solar collector, the temperature reaches a value of 79.5^(∘)C. A heat engine is operated using the collector as the hot reservoir and a cold reservoir at $298 \mathrm{~K}$. Calculate the area of the collector needed to produce 1000. W. Assume that the engine operates at the maximum Carnot efficiency.
Original LaTeX notation
The mean solar flux at Earth's surface is $\sim 2.00 \mathrm{~J}$ $\mathrm{cm}^{-2} \mathrm{~min}^{-1}$. In a nonfocusing solar collector, the temperature reaches a value of $79.5^{\circ} \mathrm{C}$. A heat engine is operated using the collector as the hot reservoir and a cold reservoir at $298 \mathrm{~K}$. Calculate the area of the collector needed to produce 1000. W. Assume that the engine operates at the maximum Carnot efficiency.

category

physics

options

  1. 16.8 $\mathrm{~m}^2$
  2. 23.5 $\mathrm{~m}^2$
  3. 18.0 $\mathrm{~m}^2$
  4. 20.5 $\mathrm{~m}^2$
  5. 21.8 $\mathrm{~m}^2$
  6. 19.4 $\mathrm{~m}^2$
  7. 17.2 $\mathrm{~m}^2$
  8. 15.6 $\mathrm{~m}^2$
  9. 24.7 $\mathrm{~m}^2$
  10. 22.3 $\mathrm{~m}^2$

src

scibench-thermo

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Source and history

upstream_id / Original problem ID
10009
task_id
d147909d-5cdf-55cd-8ad6-f6fe733f99b8
task_key
default--test--10009
task_revision_id
1
config / split
default / test

Official source

initial import