Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
Temperature and Kinetic Theory
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13-1: Atomic Theory
13-2: Temperature and Thermometers
13-4: Thermal Expansion
13-5: Gas Laws; Absolute Temperature
13-6 and 13-7: Ideal Gas Law
13-8: Ideal Gas Law in Terms of Molecules; Avogadro's Number
13-9: Molecular Interpretation of Temperature
13-11: Real Gases; Phase Changes
13-12: Vapor Pressure and Humidity
13-13: Diffusion

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 12

To what temperature would you have to heat a brass rod for it to be 1.5% longer than it is at 25C25 ^\circ \textrm{C}?

Giancoli 7th Edition, Chapter 13, Problem 12 solution video poster

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This is Giancoli Answers with Mr. Dychko. The final length of this brass rod will be the initial length plus 1.5% more than the initial length so, that's the initial length plus 0.015 times initial length which is 1.015 initial length. The change in length of the grass rod which is important because we have a formula for change in length in terms of the coefficient of linear expansion and the initial length and the change in temperature. The change in length is going to be the final length minus the initial length, and we just found the final length up there. And so that means the change is going to be 0.015 times li. That's what 1.015 minus 1 is. And then we say that... Well, since this is a change in length and this also is a change in length, those two things are equal to each other. So, α li Δt equals 0.015 li. And then divide both sides by α li. And then the li’s cancel, leaving us with the change in temperature is the 0.015 divided by the coefficient of linear expansion. So, that's 0.015 divided by 19 times 10 to the minus 6 which is 789.47 Celsius degrees. So, the final temperature will be the initial temperature of the brass rod plus this change in temperature, 25 plus 789.47. And that gives about 810 degrees Celsius will be the final temperature.

By titoarias54 on Wed, 2/5/2020 - 2:39 AM

how do you get 1.015

By preston.putzback on Tue, 11/30/2021 - 2:17 AM

that is 1.015 times the original length because it increased in length by 1.5%

By Mr. Dychko on Mon, 12/6/2021 - 3:43 PM

Thank you very much for chipping in with this great comment Preston. I appreciate it.

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