Find the change in volume for a metallic dental filling due to the difference between body temperature (37.0°C) and the temperat

Question

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Find the change in volume for a metallic dental filling due to the difference between body temperature (37.0°C) and the temperat

ure of the ice cream you ate (-6.2°C). The initial volume of the filling is 21.0 mm3, and its expansion coefficient is α = 42.0 × 10−6 K−1

Physics

1 answer:

serg [3.5K] · Answer 1 · 2026-02-27T12:58:55+03:00

Answer:

The change in the volume of a metallic dental filling caused by the temperature difference is 0.1143 mm.

Explanation:

Given:

Body temperature is, $T_1=37\ \°C$

Temperature of the ice cream is, $T_2=-6.2\ \°C$

The filling's initial volume is, $V=21.0\ mm^3$

The thermal expansion coefficient is, $\alpha =42.0\times 10^{-6}\ K^{-1}$

It is known that the coefficient of volume expansion is associated with thermal expansion as follows:

$\gamma=3\alpha=3\times 42.0\times 10^{-6}=126\times 10^{-6}\ K^{-1}$

Now, the change in volume for a metallic dental filling can be calculated as:

$\Delta V=V\gamma(T_1-T_2)\\\Delta V=21\times 126\times 10^{-6}(37-(-6.2))\\\Delta V=2646\times(37+6.2)\times 10^{-6}\\\Delta V=2646\times 43.2\times 10^{-6}\\\Delta V=0.1143\ mm^3$

Thus, the change in volume for a metallic dental filling from the temperature variance is 0.1143 mm.