## Tuesday, December 6, 2016

Kasey Halsey ’18
Thermal Physics Applied to Rings
Research has shown that swelling of the fingers can increase one’s ring size from a 0.4 inch (0.01016 meters) diameter ring to a 0.7 inch (0.01778 meters) diameter ring during summer months.1 I thought that it would be interesting to examine the thermal expansion of a rings to see how the area of the ring changes relative to the area of the finger throughout the year. We will examine the thermal expansion of the cross sectional area of the ring and compare it to the change in cross sectional area of the finger. The cross sectional area of the finger in the winter would be pi*r^2=pi*(0.01016/2)^2= 8.1*10^-5 m^2. Through a similar calculation, the cross sectional area of the finger in the summer is calculated to be 2.5*10^-4 m^2. Taking into account that the average width of a ring is 3mm (.003 meters), the true cross sectional areas of the ring (subtracting out the center) for summer and winter would be (3.4*10^-4)-(2.5*10^-4)=0.9*10^-4 m^2 and (1.4*10^-4)-(8.1*10^-5)=6.0*10^-5 m^2, respectively. Now, we know that the area of the finger changes by 3*10^-5 m^2 from winter to summer.
Now, we will look at a sterling silver ring to see how much its area will change with temperature. deltaA/A0=2(alpha)(deltaT) models the equation we would use. The thermal expansion coefficient, alpha, for sterling silver is 1.9*10-5 1/ºC.2 So, a sterling silver ring of 0.4 inch diameter, during a change of temperature of 40 ºC, would increase its area by 1.2*10^-7 m^2. This is only 4/100’s of the increase in area that we observe for the finger expansion from winter to summer, which coincides with the observation that rings do in fact get tighter during the summer; the expansion of the finger is significantly greater than the expansion of the ring.

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