# Thermal Expansion

## Homework Statement

A concrete highway is built of slabs 12 m long (20°C). How wide should the expansion cracks be (at 20°C) between the slabs to prevent buckling if the range of temperature is -30°C to +32°C?

________ cm

## Homework Equations

change in L = L original * alpha * change in temp

sorry i dont have symbols and stuff

## The Attempt at a Solution

I've tried it one way so far.

Basically, I just found the difference between the higher temp and the highway temp, and solved that as one equation. Then i found the difference between the lower temp and the highway temp, and solved that as one equation. Then i added the two answers.

change in L = 12m * 1200e-6(our teacher gave us this for alpha) * (32-20) = .1728

change in L = 12m * 1200e-6 * (20-(-30)) = .72

then i got .8928 cm

any help?

I don't think you care about how much they shrink as compared to how much the slabs expand. The big ouch comes if the slabs expand and hit each other, while if they shrink then the gap just gets a little bigger. I don't see any constraint on the overall gap size itself. Also, you should be working in Kelvin!

It seems like you shouldn't add the two. Just find the largest value (as Mindscrape said we only care about expansion) and that should be how much space you should put between the slabs. So the real problem it seems is finding the maximum value of

$$|x - 20|$$

On the range $$20 < x \le32$$

ok so something like...

change in L = 12m * 1200e-6 * 12 = .1728 cm

ohh and its 12 regardless if i work in celcius or kelvin

so does that seem better?

thanks guys i got it

Yeah, for changes in temperature the Kelvin scheme usually doesn't matter, though it did for the contraction equation you worked out because you should have got a negative when you had a positive. Get in the habit of working with Kelvin in thermo. You'll be sorry later if you don't.

Yep, that's good. Technically you should have in inequality in your answer.

Yeah, for changes in temperature the Kelvin scheme usually doesn't matter, though it did for the contraction equation you worked out because you should have got a negative when you had a positive. Get in the habit of working with Kelvin in thermo. You'll be sorry later if you don't.

Yep, that's good. Technically you should have in inequality in your answer.

He actually would have gotten a negative delta T but he switched the final and initial temperatures.