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Chapter 17: Problem 19

Suppose a bimetallic strip is constructed of two strips of metals with linear expansion coefficients \(\alpha_{1}\) and \(\alpha_{2}\), where \(\alpha_{1}>\alpha_{2}\) a) If the temperature of the bimetallic strip is reduced by \(\Delta T\), what way will the strip bend (toward the side made of metal 1 or the side made of metal 2)? Briefly explain. b) If the temperature is increased by \(\Delta T\), which way will the strip bend?

Short Answer

Expert verified
Answer: When the temperature of the bimetallic strip is decreased by \(\Delta T\), the strip will bend toward the side made of metal 1 (the metal with the higher linear expansion coefficient). When the temperature is increased by \(\Delta T\), the strip will bend away from the side made of metal 1.

Step by step solution

01

Understand what linear expansion coefficients represent

Linear expansion coefficients are measures of how much a material expands or contracts in response to a temperature change. A higher linear expansion coefficient means that the material will expand more when heated and contract more when cooled, as compared to a material with a lower expansion coefficient.
02

Determine the bending direction for a temperature decrease

Since \(\alpha_{1}>\alpha_{2}\), metal 1 will contract more than metal 2 when the bimetallic strip's temperature decreases. As a result, the strip will bend toward the side made of metal 1, as metal 1's greater contraction pulls the strip in that direction.
03

Determine the bending direction for a temperature increase

Like before, since \(\alpha_{1}>\alpha_{2}\), metal 1 will expand more than metal 2 when the bimetallic strip's temperature increases. As a result, the strip will bend away from the side made of metal 1, as metal 1's greater expansion pushes the strip in that direction.
04

Summarize the results

To summarize, when the temperature of the bimetallic strip is decreased by \(\Delta T\), it will bend toward the side made of metal 1 (with the higher linear expansion coefficient). Likewise, when the temperature is increased by \(\Delta T\), the strip will bend away from the side made of metal 1.

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Most popular questions from this chapter

a) Suppose a bimetallic strip is constructed of copper and steel strips of thickness \(1.0 \mathrm{~mm}\) and length \(25 \mathrm{~mm},\) and the temperature of the strip is reduced by \(5.0 \mathrm{~K}\). Determine the radius of curvature of the cooled strip (the radius of curvature of the interface between the two strips). b) If the strip is \(25 \mathrm{~mm}\) long, how far is the maximum deviation of the strip from the straight orientation?

Would it be possible to have a temperature scale defined in such a way that the hotter an object or system got, the lower (less positive or more negative) its temperature was?

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

One thermometer is calibrated in degrees Celsius, and another in degrees Fahrenheit. At what temperature is the reading on the thermometer calibrated in degrees Celsius three times the reading on the other thermometer?

When a 50.0 -m-long metal pipe is heated from \(10.0^{\circ} \mathrm{C}\) to \(40.0^{\circ} \mathrm{C}\), it lengthens by \(2.85 \mathrm{~cm}\). a) Determine the linear expansion coefficient. b) What type of metal is the pipe made of?
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