Thermodynamics of concrete in a highway

[newyork]

Homework Statement

Concrete highway slabs are poured in lengths of 10.0 m. How wide should the expansion gaps between the slabs be at a temperature of 20 degrees C to ensure that there will be no contact between adjacent slabs over a temperature range of -24 C to 45 C?

Homework Equations

Change in length= (coefficient of linear expansion)(initial length)(change in temp)
(I represented the coeff by α)
α of concrete=12x10^-6 degrees C^-1

The Attempt at a Solution

Change in length=(12x10^-6)(10)(-25-20)=-0.0054 m (is it ok that this is negative?)
Change in length=(12x10^-6)(10)(45-20)=0.003

Now, do I add these values to get the total change in length?
(-0.0054m)+(0.003m)= -0.0024m

I understand the equation and the idea of it, but I don't know if I solved the problem correctly.

 

[dynamicsolo]

These variations represent a shrinkage of 0.0054 m. from 10 m. when the temperature changes from 20º to -25º C and an expansion of 0.003 m. from 10 m. when the temperature goes from 20º C to 45º C. So what is the total range of length change represented here?

Oh yeah, not that it changes the result much, but the problem statement gives a minimum temperature of -24º C.

 

[merryjman]

It makes sense that one of your results is negative, because when the concrete heats up, it will expand, but if it cools down it will shrink.

 

[newyork]

These variations represent a shrinkage of 0.0054 m. from 10 m. when the temperature changes from 20º to -25º C and an expansion of 0.003 m. from 10 m. when the temperature goes from 20º C to 45º C. So what is the total range of length change represented here?

Oh yeah, not that it changes the result much, but the problem statement gives a minimum temperature of -24º C.

-0.0024m is the total range of length change represented.
sorry, I did make a typo before. -25 C to 45 C. the 20 C is right. the 24 should be 25.

 

[merryjman]

-0.0024m is the total range of length change represented.

Re-think this for a minute. If I am 6'1" in the morning, and 5'11" in the evening, but my average height is 6'0", then what is the total range of change in my height?

 

[newyork]

Re-think this for a minute. If I am 6'1" in the morning, and 5'11" in the evening, but my average height is 6'0", then what is the total range of change in my height?

You would take the difference of those values and divide by 2.

 

[merryjman]

You are right. The negative sign threw me off.

 

[dynamicsolo]

Ah, now that I went and read the question again, I see that we don't actually care what happens at -24º C... Below 20º C, the slabs will be shorter than 10 m, so we don't have to worry about them being in contact.

We are asked how big the gaps need to be at 20º C, so that they don't touch (which may be read as "just barely touch") at 45º C. You've already found that each slab expands to
10 + 0.003 m at 45º C, so if they're just touching at 45º C, how big will the gaps be at 20º C? That's the gap size you'd need to leave.

(There's a little bit of a trick to be wary of, also. Each slab is expanding in both directions, so what happens when the barely-touching slabs at 45º C cool to 20º C ?)