The graph below shows the thermal expansion of two different (hypothetical) mate

Question

The graph below shows the thermal expansion of two different (hypothetical) materials, which have the same initial length at T=100 oC. The zero of the length axis is shown, and you may take each tick mark as being 10 m. Labelled points A & B indicate exact crossings with the gridlines.

a.) Find the linear thermal expansion coefficients of each material.
(Note: you will find these values to be MUCH larger than for real materials-- this is to make the values easier to work with in this problem.)

?1 =  ??? (oC)-1
?2 =  ??? (oC)-1

b.) Occasionally, it may be useful to acknowledge that an object will not actually expand at a constant rate; the function (solid line) does curve away from its initial slope (dotted line).
Assuming that our empirical equation for thermal expansion holds, reduce it to differential form and solve for the shape of the curve. Then use it to predict the length of each material at T= 100.9 oC.

L1 = ??? m
L2 =  ??? m

Explanation / Answer

Alpha 2 = (40.1 -10)/(10 * 101.-4)

A2 = 3 e-2 per degC

--------------------------------------------

use L2 = L1 + A DT

for material #1, L2 = 10 + ( 0.0198* 100.9)

L2 = 12 m

for material #2, L2 = 10 + ( 0.03* 100.9)

L2 = 13.02 m

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