Explanation Description: The solid rod expands thermally when it is heated to a from temperature value to the high temperature value. The rod’s length, area, and volume change from initial value to the final value. Write the expression for the coefficient of linear expansion (change in length) of the rod as follows. Δ l = α l Δ T (1) Here, Δ l is the rod’s change in length, α is the rod’s coefficient of linear expansion, l is the rod’s original length, and Δ T is change in the temperature (temperature variation). Write the expression for variation in the temperature as follows. Δ T = T f − T i (2) Here, T i is the initial temperature, and T f is the final temperature. Calculation of coefficient of linear expansion for the solid rod ( α ) : Consider the rod’s original length, change in the length, initial temperature, and final temperature for the sample calculation as follows. l = 50.0 m Δ l = 0.2 m T i = 15.0 ° C T f = 130 ° C From equation (2), substitute ( T f − T i ) for Δ T in equation (1) to obtain the following expression. Δ l = α l ( T f − T l ) Rearrange the expression for coefficient of linear expansion as follows. α = Δ l l ( T f − T l ) Substitute 0.2 m for Δ l , 50.0 m for l , 15.0 ° C for T i , and 130.0 ° C for T f to obtain the coefficient of linear expansion of the rod. α = 0.2 m ( 50.0 m ) ( 130 ° C − 15.0 ° C ) = 3.4782 × 10 − 5 1 / ° C ≅ 3.5 × 10 − 5 1 / ° C From the calculation, the coefficient of linear expansion for the rod is 3.5 × 10 − 5 1 / ° C . Calculation of coefficient of area expansion for the rod ( β ) : Write the expression for the coefficient of area expansion (change in area) of the rod as follows. Δ A = β A Δ T (3) Here, Δ A is the change in rod’s area, β is the rod’s coefficient of area expansion, and A is the rod’s original area. Rearrange the expression in equation (3) for coefficient of area expansion as follows. β = Δ A A Δ T β = Δ A A ( T f − T l ) (4) Consider the rod’s original area, and change in the area for the sample calculation as follows. A = 50

Thinking Like An Engineer: An Active Learning Approach, Student Value Edition (4th Edition)

4th Edition

ISBN: 9780134640150

Author: STEPHAN, Elizabeth A.; Bowman, David R.; Park, William J.; Sill, Benjamin L.; Ohland, Matthew W.

Publisher: PEARSON

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Thermodynamic Relations

Thermodynamics is the division of physics that deals with the transfer of any kind of energy, whether it be heat, temperature, or work, from one object to another.

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Chapter 3, Problem 16MDP

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Find the coefficient of thermal expansion of a solid bar or rod.

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Chapter 3, Problem 15MDP

Chapter 3, Problem 18MDP

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Thinking Like An Engineer: An Active Learning Approach, Student Value Edition (4th Edition)

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