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MMLU-Pro / 7882 / Let a metallic rod 20 mathrm{~cm} long be heated to a uniform temperature of…

Problem

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

question

Let a metallic rod $20 \mathrm{~cm}$ long be heated to a uniform temperature of 100∘C100^{\circ} \mathrm{C}. Suppose that at t=0t=0 the ends of the bar are plunged into an ice bath at 0∘C0^{\circ} \mathrm{C}, and thereafter maintained at this temperature, but that no heat is allowed to escape through the lateral surface. Determine the temperature at the center of the bar at time $t=30 \mathrm{~s}$ if the bar is made of silver.
Plain-text mathematical notation (without MathML)
Let a metallic rod $20 \mathrm{~cm}$ long be heated to a uniform temperature of 100^(∘)C. Suppose that at t=0 the ends of the bar are plunged into an ice bath at 0^(∘)C, and thereafter maintained at this temperature, but that no heat is allowed to escape through the lateral surface. Determine the temperature at the center of the bar at time $t=30 \mathrm{~s}$ if the bar is made of silver.
Original LaTeX notation
Let a metallic rod $20 \mathrm{~cm}$ long be heated to a uniform temperature of $100^{\circ} \mathrm{C}$. Suppose that at $t=0$ the ends of the bar are plunged into an ice bath at $0^{\circ} \mathrm{C}$, and thereafter maintained at this temperature, but that no heat is allowed to escape through the lateral surface. Determine the temperature at the center of the bar at time $t=30 \mathrm{~s}$ if the bar is made of silver.

category

math

options

  1. 42.58 ${ }^{\circ} \mathrm{C}$
  2. 35.91 ${ }^{\circ} \mathrm{C}$
  3. 30.48 ${ }^{\circ} \mathrm{C}$
  4. 40.32 ${ }^{\circ} \mathrm{C}$
  5. 45.78 ${ }^{\circ} \mathrm{C}$
  6. 55.12 ${ }^{\circ} \mathrm{C}$
  7. 50.25 ${ }^{\circ} \mathrm{C}$
  8. 60.89 ${ }^{\circ} \mathrm{C}$
  9. 38.76 ${ }^{\circ} \mathrm{C}$
  10. 25.67 ${ }^{\circ} \mathrm{C}$

src

scibench-diff

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Source and history

upstream_id / Original problem ID
7882
task_id
c20011d9-4a6e-5eb3-b597-e6ea358cf051
task_key
default--test--7882
task_revision_id
1
config / split
default / test

Official source

initial import