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Difficulty: HardThermal Expansion and Contraction

A temperature sensor utilizes a bimetallic strip composed of a top layer of brass and a bottom layer of steel, which are permanently bonded together. Brass has a significantly higher coefficient of thermal expansion than steel. If the strip is perfectly straight at room temperature, what will happen to its physical shape when it is exposed to sub-zero temperatures?

  1. It bends into a curve with the brass layer on the inside radius.Answer
  2. B
    It bends into a curve with the steel layer on the inside radius.
  3. C
    It remains completely straight but decreases in overall length.
  4. D
    It remains completely straight and increases in overall length.

Answer

The strip bends into a curve with the brass layer on the inside radius.
When cooled, metals contract. Because brass has a higher coefficient of thermal expansion than steel, it contracts (shrinks) significantly more than steel for the same drop in temperature. Since the two layers are permanently bonded, the shorter brass layer pulls the strip into a curve, acting as the inner, shorter radius of that curve.

Step-by-Step Solution

1
Identify the temperature change.
The strip is exposed to sub-zero temperatures, meaning it is being cooled.
Cooling causes most metals to contract (shrink) rather than expand.
2
Compare the contraction rates of the two metals.
Because brass has a higher coefficient of thermal expansion than steel, it will contract more than steel when cooled.
The coefficient of thermal expansion dictates the rate of both expansion during heating and contraction during cooling.
3
Determine the physical effect on the bonded strip.
The brass layer becomes shorter than the steel layer. Because they are permanently bonded, the strip must curve to accommodate the different lengths.
Bonded materials with unequal lengths naturally form an arc to relieve internal stress.
4
Identify the inner and outer layers of the resulting curve.
The shorter layer (brass) forms the inside of the curve, while the longer layer (steel) forms the outside.
Geometrically, the inner radius of any curve has a shorter path length than its outer radius.

Key Concept

Differential Thermal Contraction in Bimetallic Strips
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Topics

Thermal Expansion and Contraction

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