The question: At 21°C, a rod is exactly 20.09 cm long on a steel ruler. Both the

Question

The question:

At 21°C, a rod is exactly 20.09 cm long on a steel ruler. Both the rod and theruler are placed in an oven at 243°C, where the rod nowmeasures 20.24 cm on the same ruler. Whatis the coefficient of linear expansion for the material of whichthe rod is made?

For this question, I understand that as both the rod and the steelruler are expanding, the measurement of the rod after being placedin the oven is not exact, as the ruler, too, has expanded. What Idon't get is how come the solution given here states the initialsize of the steel ruler as being what the rod is now afterexpansion? I do not understand if this is an assumption, or if itis the actual initial length of the ruler. I would appreciate ifanyone could clear up my confusion.

PLEASE do NOT solve this problem for me. I'm not asking for someoneto solve, just to explain how we get the initial length of thesteel ruler.

Explanation / Answer

TO ANSWER YOUR QUESTION... . The length of the entire steel ruler is arbitrary... they donttell you it is a "one meter long" steel ruler, or something likethat. And it doesn't matter! You have a length of steel which ismarked in increments of centimeters. Make that piece of steel aslong as you like. . One way to address the problem is to just give yourself a setlength... make it a 100 cm long steel ruler. Then you can modifythe wording of the problem so that the rod is 20.09 % of the length of the ruler, initially. This means that, when youlay the rod against the ruler, the rod is even with the 20.09cm mark. . Then you can find how much each expands and find the ratio ofthe length of the rod to ruler at the higher temperature. No matterwhat length of ruler you choose, how that ratio changes from coldto hot will be the same.

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