Question

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 (-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

Answer 1

Answer:

The change in volume for a metallic dental filling due to the temperature difference is 0.1143 mm.

Explanation:

Given:

Temperature of the body is, $T_1=37\ \°C$

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

Initial volume of the filling is, $V=21.0\ mm^3$

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

We know that the coefficient of volume expansion is related to thermal expansion as:

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

Now, change in volume for a metallic dental filling is given as:

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

Therefore, the change in volume for a metallic dental filling due to the temperature difference is 0.1143 mm.