What Temperature Causes a Steel Ball to Loosen in a Pyrex Cube?

AI Thread Summary
The discussion centers on determining the temperature at which a steel ball bearing, tightly fitting inside a Pyrex glass cube, will have a clearance of 0.90 picometers. The coefficient of linear expansion for Pyrex is given as 3.2e-6, but the user is unsure how to calculate the change in length (Delta L) needed for their solution. They have established the initial dimensions and temperature, with the cube measuring 1.0 cm on each side and starting at 390K. A comparison of the expansion coefficients of Pyrex and steel is also sought to aid in the calculations. The resolution hinges on calculating Delta L to find the final temperature.
Lance WIlliam
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Homework Statement



A steel ball bearing is encased in a Pyrex glass cube 1.0 cm on a side. At 390K , the ball bearing fits tightly inside the cube.

At what temperature will it have a clearance of 0.90pico meters all around?


Homework Equations


Coefficent of linear expansion:
\propto =(Change in L / L) / change in T

Im not sure what my Delta L should be...
L= .01 m
T initial is 390K
the \propto is 3.2e-6


The Attempt at a Solution



I just need delta L in order to solve for T final
 
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How does the expansion coefficient of Pyrex compare to that of steel?
 
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