Linear Thermal Expansion: Bridge Joints

[Warden619]

SOLVED

Homework Statement

A bridge is made with segments of concrete 80 m long (at the original temperature).
If the linear expansion coefficient is 1.2 x 10^-5 (1/degrees C), how much spacing is
needed to allow for expansion for an increase in temperature of 50 degrees F? Answer in units of cm.

Homework Equations

$$\Delta$$L = $$\alpha$$ L(0) $$\Delta$$T

Degrees F = [(9/5) x Degrees C] + 32

The Attempt at a Solution

This should be so simple...
Degrees in C is simply (50-32) / (9/5) = 10 degrees C (This is delta T)
Convert 80 meters to 8000 cm.

So just plug and chug...

$$\Delta$$L = (1.2 x 10^-5) (8000) (10)
= 0.96 cm

If the bridge is composed of two segments, then each one will expand 0.96, so you would need 1.92 cm of space according to my work.

But the solutions manual says the answer is 2.6667 cm. This has been driving me up the wall, any assistance would be appreciated.

 

[Mapes]

Hi Warden619, welcome to PF. 50°F absolute is 10°C absolute, but a difference of 50°F is not a difference of 10°C. Know what I mean?

 

[Warden619]

So then the actual change in temperature is simply 50 / (9/5) = 27.777. We just throw out the 32 from the formula. Thank you very much, I knew it had to be something simple I was missing.

 

[Mapes]

My pleasure.