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Chapter 17: Problem 4

Which of the following bimetallic strips will exhibit the greatest sensitivity to temperature changes? That is, which one will bend the most as temperature increases? a) copper and steel b) steel and aluminum c) copper and aluminum d) aluminum and brass e) copper and brass

Short Answer

Expert verified
Answer: b) steel and aluminum

Step by step solution

01

1. Obtain the coefficients of linear expansion

First, we must obtain the coefficients of linear expansion for each of the metals, copper (Cu), steel (St), aluminum (Al), and brass (Br). The coefficient of linear expansion, α, is a measure of how much the metal expands per degree Celsius in change of temperature. The values are as follows: Cu: α = 17 x 10^{-6} °C^{-1} St: α = 11 x 10^{-6} °C^{-1} Al: α = 23 x 10^{-6} °C^{-1} Br: α = 19 x 10^{-6} °C^{-1}
02

2. Calculate differences in coefficients of linear expansion

Next, we'll find the difference in the coefficients of linear expansion for each of the given bimetallic strip combinations: a) Cu-St: |17 x 10^{-6} - 11 x 10^{-6}| = 6 x 10^{-6} °C^{-1} b) St-Al: |11 x 10^{-6} - 23 x 10^{-6}| = 12 x 10^{-6} °C^{-1} c) Cu-Al: |17 x 10^{-6} - 23 x 10^{-6}| = 6 x 10^{-6} °C^{-1} d) Al-Br: |23 x 10^{-6} - 19 x 10^{-6}| = 4 x 10^{-6} °C^{-1} e) Cu-Br: |17 x 10^{-6} - 19 x 10^{-6}| = 2 x 10^{-6} °C^{-1}
03

3. Identify the greatest difference

Now we can identify the greatest difference in coefficients of linear expansion, which corresponds to the maximum sensitivity to temperature change: The greatest difference is 12 x 10^{-6} °C^{-1}, which corresponds to the bimetallic strip made of steel and aluminum (option b). So, the bimetallic strip with the greatest sensitivity to temperature changes is b) steel and aluminum.

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Most popular questions from this chapter

The lowest air temperature recorded on Earth is \(-129^{\circ} \mathrm{F}\) in Antarctica. Convert this temperature to the Celsius scale.

How does the density of copper that is just above its melting temperature of \(1356 \mathrm{~K}\) compare to that of copper at room temperature?

Two solid objects, \(A\) and \(B\), are in contact. In which case will thermal energy transfer from \(\mathrm{A}\) to \(\mathrm{B} ?\) a) \(\mathrm{A}\) is at \(20{ }^{\circ} \mathrm{C},\) and \(\mathrm{B}\) is at \(27{ }^{\circ} \mathrm{C}\) b) \(A\) is at \(15^{\circ} \mathrm{C},\) and \(\mathrm{B}\) is at \(15^{\circ} \mathrm{C}\). c) \(\mathrm{A}\) is at \(0{ }^{\circ} \mathrm{C},\) and \(\mathrm{B}\) is at \(-10{ }^{\circ} \mathrm{C}\).

On a hot summer day, a cubical swimming pool is filled to within \(1.0 \mathrm{~cm}\) of the top with water at \(21{ }^{\circ} \mathrm{C} .\) When the water warms to \(37^{\circ} \mathrm{C}\), the pool overflows. What is the depth of the pool?

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