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Difficulty: Very hardThermodynamics and Heat

A scientist suspends two metal blocks of equal mass, Block X and Block Y, by thin insulating threads inside a completely evacuated vacuum chamber. The chamber walls are maintained at 0°C, and both blocks are initially at 100°C. Block X has a matte black surface and a low specific heat capacity. Block Y has a highly polished, shiny surface and a high specific heat capacity. Which of the following correctly identifies the exclusive mechanism of heat transfer from the blocks to the chamber walls, and which block will reach 0°C first?

  1. Radiation; Block X will reach 0°C first.Answer
  2. B
    Convection; Block Y will reach 0°C first.
  3. C
    Radiation; Block Y will reach 0°C first.
  4. D
    Conduction; Block X will reach 0°C first.

Answer

Radiation is the exclusive heat transfer mechanism, and Block X will reach 0°C first.
In a vacuum, there is no physical matter to transfer heat, meaning conduction and convection are impossible; therefore, radiation is the only method of heat transfer. Block X will cool faster for two compounding reasons: its matte black surface makes it a significantly better emitter of thermal radiation than the polished Block Y, and its lower specific heat capacity means it requires less total thermal energy loss to drop its temperature.

Step-by-Step Solution

1
Determine the mechanism of heat transfer.
The mechanism must be radiation.
The chamber is a completely evacuated vacuum. Conduction and convection require matter (particles) to transfer heat, leaving radiation as the only possible method.
2
Analyze the effect of the surface finishes on the cooling rate.
Block X emits thermal energy faster than Block Y.
Matte black surfaces (Block X) are excellent emitters of thermal radiation, whereas highly polished surfaces (Block Y) are poor emitters that reflect radiation internally.
3
Analyze the effect of specific heat capacity on the cooling rate.
Block X requires less energy loss to drop in temperature.
A low specific heat capacity means a substance requires less heat transfer to change its temperature. Therefore, Block X's temperature drops more rapidly for a given amount of heat lost.
4
Combine findings to determine which block cools first.
Block X will reach 0°C first.
Block X is losing heat at a faster rate (due to its emissive surface) AND requires less heat loss to drop its temperature (due to its low specific heat capacity). These factors compound to make it cool much faster than Block Y.

Key Concept

Heat Transfer in a Vacuum and Thermal Properties
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Topics

Thermodynamics and Heat

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