A certain steel tape, for which the coefficient of expansion is 0.00000645, is exactly 100ft long at 68F.?

Question

At 15F the length of the tape is.....(how many feet)

Answer 1

The coefficient of thermal expansion is a unit- per -unit change. In this case the units are feet and the amount of this unit change in length will be 6.45(10^-6) ft. per each ft. of length per each Fdeg. of change
The F deg change is 68-15 = 53
The unit change is 6.45(10^-6) (53) = 341.85 (10^-6) ft. per ft.
The total change is 100 x 342 (10^-6)= 0.0342 Ft (rounded-off)
Since the temperature was reduced, this is a contraction and the tape will now be 100 - 0.0342 = 99.966 ft long.
It will have shrunk a little less than 1/2 inch. (0.41")

Answer 2

Thermal expansion is fairly simple to calculate for this.

Change in Length = (Coefficient * Change in Temperature)

Change in Temperature = 15-68 = -53

Change in Length = (.00000645 * -53) = -0.00034185 ft

Subtract this from the original length, and you should have your length at 15 degrees.

The coefficient seems rather low, though.

Answer 3

You need to define your coefficient better. Assuming you actually mean that the coefficient is defined as "inches per degree Fahrenheit":

(New length) = (old length)-(coefficient)*(change in temperature)
(New length) = (100) - (0.00000645) * (68-15) = 99.999658 feet

Answer 4

At what temperature?