Thermodynamics (Heat expansivity)

[Aleisha]

Homework Statement

A concrete driveway is built from identical slabs of concrete, as shown below, which have a length, L, of 3.18 m long at 17.3 C. The concrete slabs have coefficient of linear expansion of 1.20 x 10-5 K-1 and are laid in an area where the temperature ranges from -29.8 C to 42.6 C.
Calculate the minimum lengthwise gap (Δx) that should be left between the tiles when they are laid to ensure that the tiles do not buckle when the temperature changes.

Homework Equations

Change in length=coefficient of linear expansion x original length x change in temp (Kelvin)

The Attempt at a Solution

Change in length (x)= (1.20e-5) x 3.18 x 72.4
=2.76e-3m
Answer was wrong but am confused as to how else to do it with any other equation i think i may have made an error with conversions or values needing to be used?

 

[Chestermiller]

Homework Statement

A concrete driveway is built from identical slabs of concrete, as shown below, which have a length, L, of 3.18 m long at 17.3 C. The concrete slabs have coefficient of linear expansion of 1.20 x 10-5 K-1 and are laid in an area where the temperature ranges from -29.8 C to 42.6 C.
Calculate the minimum lengthwise gap (Δx) that should be left between the tiles when they are laid to ensure that the tiles do not buckle when the temperature changes.

Homework Equations

Change in length=coefficient of linear expansion x original length x change in temp (Kelvin)

The Attempt at a Solution

Change in length (x)= (1.20e-5) x 3.18 x 72.4
=2.76e-3m
Answer was wrong but am confused as to how else to do it with any other equation i think i may have made an error with conversions or values needing to be used?

The slabs are laid at 17.3 degrees. If the temperature goes down to -29.8 C, the slabs get shorter so they can't buckle. They can only get longer at temperatures above 17.3 C.

 

[Aleisha]

So technically to get the correct answer i have to minus 17.3 from the highest temp i.e. 42.6-17.3=25.3 C? And that will be my change in temp and everything else stays the same?

 

[Chestermiller]

So technically to get the correct answer i have to minus 17.3 from the highest temp i.e. 42.6-17.3=25.3 C? And that will be my change in temp and everything else stays the same?

Yes. But, you need to take into account that both slabs grow by this amount. On the other hand, they didn't tell you where the slabs are anchored. I guess you need to assume that they are anchored at their opposite ends.

 

[Aleisha]

Thank you!