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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 background temperature of the universe is a) \(6000 \mathrm{~K}\). b) \(288 \mathrm{~K}\). c) \(3 \mathrm{~K}\). d) \(2.73 \mathrm{~K}\). e) \(0 \mathrm{~K}\).

Two mercury-expansion thermometers have identical reservoirs and cylindrical tubes made of the same glass but of different diameters. Which of the two thermometers can be graduated to a better resolution? a) The thermometer with the smaller diameter tube will have better resolution. b) The thermometer with the larger diameter tube will have better resolution. c) The diameter of the tube is irrelevant; it is only the volume expansion coefficient of mercury that matters. d) Not enough information is given to tell.

Express each of the following temperatures in degrees Celsius and in kelvins. a) \(-19^{\circ} \mathrm{F}\) b) \(98.6^{\circ} \mathrm{F}\) c) \(52^{\circ} \mathrm{F}\)

The volume of \(1.00 \mathrm{~kg}\) of liquid water over the temperature range from \(0.00^{\circ} \mathrm{C}\) to \(50.0^{\circ} \mathrm{C}\) fits reasonably well to the polynomial function \(V=1.00016-\left(4.52 \cdot 10^{-5}\right) T+\) \(\left(5.68 \cdot 10^{-6}\right) T^{2}\), where the volume is measured in cubic meters and \(T\) is the temperature in degrees Celsius. a) Use this information to calculate the volume expansion coefficient for liquid water as a function of temperature. b) Evaluate your expression at \(20.0^{\circ} \mathrm{C}\), and compare the value to that listed in Table \(17.3 .\)

On a cool morning, with the temperature at \(15.0^{\circ} \mathrm{C}\), a painter fills a 5.00 -gal aluminum container to the brim with turpentine. When the temperature reaches \(27.0^{\circ} \mathrm{C}\), how much fluid spills out of the container? The volume expansion coefficient for this brand of turpentine is \(9.00 \cdot 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\).
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