Question

Required Information
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

Answer 1

Answer:

$\Delta V=-18,62784\ mm^3$

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 $\alpha$, an initial volume $V_o$ to an initial temperature $T_o$ which is later to a final temperature $T_f$

The change in volume due to thermal expansion is

$\Delta V=3\alpha V_o (T_f-T_o)$

The teeth filling has an initial volume of

$V_o=320\ mm^3$

At a temperature of

$T_o=37\ ^oC$

Its linear thermal expansion coefficient is

$\alpha=420x10^{-6}\ ^oK^{-1}$

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

$T_f=-9.2\ ^oC$

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

$T_o=37^oC-273.15=-236.15^oK$

$T_f=-9.2^oC-273.15=-282.35^oK$

Thus we have

$\Delta V=3(420x10^{-6}\ ^oK^{-1}) (320\ mm^3) (-282.35^oK+236.15^oK)$

$\Delta V=0,4032\ mm^3(-46.2^oK)$

$\Delta V=-18,62784\ mm^3$

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

Answer 2

The change in the volume defines the difference in the volume between the two conditions. The change in volume for a metallic dental filling will be -18,62784 mm³.

What is thermal expansion?

The expansion of any material due to the thermal application is known as the thermal expansion.

The given data in the problem is;

Δv is the change in the volume =?

$\rm T_f$ is the body temperature = 37.0°C

$\rm T_i$ is the temperature of ice cream you ate (-9.2°C)

α is the expansion coefficient= 420 x 10⁻⁶ K⁻¹ mm

The change in the volume due to the thermal expansion is given by;

$\triangle v = 3 \alpha V_0 (T_f-T_i)\\\\ \triangle v = 3 (420 \times 10^{-6} \times 320 \times (-282.35 ^0c+ 236.15 ^0)\\\\ \triangle v = 0.4032 \times (-46.2) \\\\ \triangle v = -18,62784\ mm^3$

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