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(Solved): If a cylindrical rod of nickel 100.00mm long and 8.100mm in diameter is heated from 20 ...
If a cylindrical rod of nickel long and in diameter is heated from to while its ends are maintained rigid, determine its change in diameter. You may want to consult Table 6.1 and Table 19.1. Part 1 What is the change in diameter, in , from only the change in temperature? Attempts: 0 of 5 used Part 2 How much will the diameter change, in , from only the stress induced because the sample is constrained while it is being heated?
How much will the diameter change, in , from only the stress induced because the sample is constrained while it is being heated? Click here for Table 6.1. Attempts: 0 of 5 used What is the total change in diameter, in , considering both the induced stress and the change in temperature (see Steps 1 and 2)?
Expert Answer
Change in diameter: temperature: To determine the change in diameter of the nickel rod due to the change in temperature, we can use the coefficient of linear expansion and the formula for thermal expansion. According to Table 6.1, the coefficient of linear expansion (?) for nickel is approximately First, let's calculate the change in length of the rod using the formula: Where: ?L is the change in length ? is the coefficient of linear expansion L is the original length of the rod ?T is the change in temperature Given: L = 100.00 mm (length of the rod) (change in temperature) Substituting the values, we have: The change in length of the rod due to the change in temperature is 0.01862 mm. Next, let's calculate the change in diameter. Since the rod is cylindrical, the change in diameter is equal to twice the change in length: Therefore, the change in diameter of the nickel rod, caused by the change in temperature, is approximately 0.03724 mm.