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suppose you have a filling in one of your teeth, and, while eating some ice cream, you suddenly realize that the filling
came out. one of the reasons the filling may have become detached from your tooth is the differential contraction of the
filling relative to the rest of the tooth due to the temperature change.
find the change in volume for a metallic dental filling due to the difference between body temperature (37.0°c) and the temperature of
the ice cream you ate (-9.2°c). the initial volume of the filling is 320 mm, and its expansion coefficient is a = 420 x 10-6k-1
mm

Explanation:

The question can be answered by using the thermal expansion theory. We need to use the formulas for the volume expansion.

Let's assume we have some material with a linear thermal expansion coefficient , an initial volume to an initial temperature which is later to a final temperature

The change in volume due to thermal expansion is

The teeth filling has an initial volume of

At a temperature of

Its linear thermal expansion coefficient is

The final temperature of the ice cream which caused the filling to come out was

Since the thermal coefficient is expressed in reciprocal Kelvin degrees, we need to convert the temperatures to

Thus we have

This differential contraction of the filling relative to the rest of the tooth caused the event

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