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MMLU-Pro / 9497 / A wire 0.5 mm in diameter is stretched along the axis of a cylinder 5 cm in…

Problem

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

question

A wire 0.5 mm in diameter is stretched along the axis of a cylinder 5 cm in diameter and 25 cm in length. The wire is maintained at a temperature of 750°K by passing a current through it, the cylinder is kept at 250°K, and the gas in it has a thermal conductivity of 6 × 10^-5 cal\bulletcm^-1\bulletC deg^-1\bulletsec^-1. Find the rates at which the heat is dissipated both by conduction through the gas and by radiation, if the wire is perfectly black.

category

physics

options

  1. 0.7 cal s^-1 by conduction, 1.2 cal s^-1 by radiation
  2. 0.6 cal s^-1 by conduction, 1.5 cal s^-1 by radiation
  3. 0.8 cal s^-1 by conduction, 1.3 cal s^-1 by radiation
  4. 1.1 cal s^-1 by conduction, 2.2 cal s^-1 by radiation
  5. 2.5 cal s^-1 by conduction, 2.7 cal s^-1 by radiation
  6. 1.2 cal s^-1 by conduction, 1.8 cal s^-1 by radiation
  7. 1.5 cal s^-1 by conduction, 2.0 cal s^-1 by radiation
  8. 0.95 cal s^-1 by conduction, 1.50 cal s^-1 by radiation
  9. 1.02 cal s^-1 by conduction, 1.67 cal s^-1 by radiation
  10. 1.3 cal s^-1 by conduction, 1.9 cal s^-1 by radiation

src

stemez-Physics

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Source and history

upstream_id / Original problem ID
9497
task_id
f5706668-89d0-52c8-ac94-9a28ae734dcb
task_key
default--test--9497
task_revision_id
1
config / split
default / test

Official source

initial import