Quandaries and Queries


Hi Math Central,

Is the following statement true?

The coefficient of thermal expansion for steel is 0.00000645in/in/deg F. Doesn't sound like much but when you run out the numbers it comes to .405504 ft/mile/deg. Still doesn't sound like much, only about 5". Then multiply by 40 degrees and you get a piece of rail that has grown by 16.22 feet in that one mile. It's not at all unusual for the rail temp to go from say, 40 deg to 80 deg on a spring or fall day. Remember that on a sunny day, the rail temp can be significantly higher than the air temp as well."

I ran the math and came up with an answer closer to 16 inches, instead of 16 feet. Which is closer to being correct ?

Thanks, Jim



Hi Jim,

I agree with you. One mile is 5280 feet so one mile is 12 5280 = 63360 inches. One inch of steel will expand 0.00000645 inches for every degree Fahrenheit increase in temperature so 63360 inches will expand

63360 0.00000645 = 0.408672 inches per degree.

Hence a 40 degree increase in temperature will result in an expansion of

40 0.408672 = 16.35 inches.