A brass washer has an inside diameter of 2.000 cm and an outside diameter of 3.0
ID: 581245 • Letter: A
Question
A brass washer has an inside diameter of 2.000 cm and an outside diameter of 3.000 cm at 20.0 degrees Celsius. A solid rod of aluminum has a diameter of 2.000 cm at 20.0 degrees Celsius and just fits inside the washer as shown in Figure 24-2. Both the washer and aluminum rod are raised to a temperature of 150.0 degrees Celsius. Will the rod still fit inside the washer? If so how much smaller is the rod than the opening in the washer? If not, how much larger is the rod than the opening in the washer? Show your work.
Explanation / Answer
Thermal Expansion Coefficients at 20 C
brass ------- = 19 10^-6 °/C
aluminum--- = 24 10^-6 °/C
t = 150 -20 = 130°C
brass washer
d = d° t = 2 * 19 10^-6 * 130 = 4940 10^-6 =+ 4.94 10^-3 cm
diameter brass washer = 2 + 4.94 10^-3 = 2.00494 cm
Rod aluminium
d = d° t = 2 * 24 10^-6 * 130 = 6240 10^-6 = + 6.24 10^-3 cm
diameter rod = 2 + 6.24 10^-3 = 2.00624 cm
diameter rod Bigger hole brass washer 2.00624 - 2.00494 = 0.0013 cm = 0.013 mm
The rod cannot go into the slice
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