Coefficient of Linear Expansion

[Sonek]

Homework Statement

Original Length = 6.736 mm
Final Length = 7.802 mm
Initial Temp = 21.7 C
Final Temp = 99.5 C

Homework Equations

Coefficient = (Change in Length) / (Original Length * Change in Temperature)

The Attempt at a Solution

Change in Length = 7.802 - 6.736 = 1.066 mm
1.066 mm = .001066 m

Change in Temp = 99.5 - 21.7 = 77.8 C1

Coefficient = (.001066) / (.006736 * 77.8 ) = 0.002034 = 2.034 x 10^-4

My units are all in meters and degrees C, but my coefficient is off. It should be in the area of 10^-6 not 10^-4. The measurements are taken from a lab we performed and the rod was solid not a gas or liquid. Help?

 

[haruspex]

It's worse than you think: 0.002034 = 2.034 x 10^-3.
I see nothing else wrong with your calculations, so either it's the right answer or you made a bad measurement. What was the rod made of?

 

[Sonek]

I was leaning towards aluminum because it had the closest co-efficient and I figured I was messing up the units someplace. I guess my lab group read the micrometer wrong.

 

[haruspex]

You could try guessing the error is in the leading digit of one measurement. That will put it in the right ballpark, but give two possibilities.

 

[Sonek]

I'm not sure what you meant haruspex, changing the leading digit didn't change the magnitude only the leading value. The coefficient changed from 2.034 x 10^-3 to 4.623x 10^-3 or 3.942 x 10^-3.

Recorded Values Hypothesis 1 Hypothesis 2
Original Length 6.736 mm Original Length 5.736 mm 6.736 mm
Final Length 7.802 mm Final Length 7.802 mm 8.802 mm
Initial Temp 21.7 C Initial Temp 21.7 C 21.7 C
Final Temp 99.5 C Final Temp 99.5 C 99.5 C
Change in Length 1.066 mm Change in Length 2.066 mm 2.066 mm
Change in Temp 77.8 C Change in Temp 77.8 C 77.8 C
Coefficient 2.034 x 10^-3 Coefficient 4.623x 10^-3 3.942 x 10^-3

 

[haruspex]

No, I meant change the leading digit of one of the two lengths to match the other measurement.

 

[Sonek]

No dice. With the change in length set at 0.066 mm, the co-efficient is still only 1.259 x 10^-4. Two orders of magnitude too high.

 

[Chestermiller]

The change in length is way too big. You must have made a mistake in recording either the original length of the final length. Is it possible that the original length was 7.736 mm, rather than 6.736 mm? Is it possible that the final length was 6.802 mm, rather than 7.802 mm? In either of these cases, the change in length would have been only 0.066mm, rather than 1.066 mm.