Respuesta :
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, [tex]T_1=37\ \°C[/tex]
Temperature of the ice-cream is, [tex]T_2=-6.2\ \°C[/tex]
Initial volume of the filling is, [tex]V=21.0\ mm^3[/tex]
Coefficient of thermal expansion is, [tex]\alpha =42.0\times 10^{-6}\ K^{-1}[/tex]
We know that the coefficient of volume expansion is related to thermal expansion as:
[tex]\gamma=3\alpha=3\times 42.0\times 10^{-6}=126\times 10^{-6}\ K^{-1}[/tex]
Now, change in volume for a metallic dental filling is given as:
[tex]\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[/tex]
Therefore, the change in volume for a metallic dental filling due to the temperature difference is 0.1143 mm.
The changes in volume for a metallic dental filling due to the difference between body temperature will be 0.1143 mm.
What is thermal expansion?
The expansion of any material due to the thermal application is known as thermal expansion.
The given data in the problem is;
Δv is the change in the volume =?
T₂ is the body temperature = 37.0°C
T₁ is the temperature of ice cream you ate (-6.2°C)
α is the expansion coefficient= 42.0 x 10⁻⁶ K⁻¹ mm
The coefficient of the volume expansion is given by;
[tex]\gamma = 3 \alpha \\\\ \gamma = 3 \times 42.0 \times 10^{-6} \\\\ \gamma = 126 \times 10^{-6}[/tex]
The change in the volume due to the thermal expansion is given by;
[tex]\triangle v = V \gamma (T_2-T_1) \\\\ \triangle v = 21 \times 126 \times 10^{-6} (37-(-6.2))\\\\ \triangle v = 2646 \times (37+6.2)\times 10^{-6} \\\\ \triangle v = 0.0143\ mm^3[/tex]
Hence the changes in volume for a metallic dental filling will be -18,62784 mm³.
To learn more about the thermal expansion refer to the link;
https://brainly.com/question/26046548
