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

VIDEO TRANSCRIPT

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.