Question

A student walking to class on a cold day (T=0 C) finds a silver ring with an inner diameter of D=1.8 cm. The silver has a coefficient of expansion of a=18.7 x 10^-6

a) Input an expression for the rings inner diameter Dh when the student warms it up to their body temperature, Tb.

b)What is the change in diameter in mm if Tb = 37 C

Answer 1

Answer on Question #57792, Physics – Molecular Physics | Thermodynamics

A student walking to class on a cold day (T=0 C) finds a silver ring with an inner diameter of D=1.8 cm. The silver has a coefficient of expansion of a=18.7 x 10^-6

a) Input an expression for the rings inner diameter $D_h$ when the student warms it up to their body temperature, $T_b$.

b) What is the change in diameter in mm if $T_b = 37{}^\circ C$

Solution:

a)

The hole in ring expands as if were filled with silver, so the change in the diameter is given by

$$\Delta D = \alpha D_0 \Delta T,$$

where $\alpha = 18.7 \times 10^{-6}$ is the coefficient of linear expansion, $D_0$ is the original diameter, and $\Delta T$ is the change in temperature.

b)

Hence, the change in the ring's diameter is

$$\Delta D = \alpha D_0 \Delta T = (18.7{}^\circ C \cdot 10^{-6}) (1.8{}^\circ C \cdot 10^{-2} \text{ m}) (37{}^\circ C - 0{}^\circ C) = 12.4542{}^\circ C \cdot 10^{-6} \text{ m} \approx 0.0125 \text{ mm}$$

Answer: 0.0125 mm

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