Question

Required Information

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