Chapter 02.03 Differentiation of Discrete Functions-More Examples Mechanical Engineering Example 1 To find the contraction of a steel cylinder immersed in a bath of liquid nitrogen, one needs to know the thermal expansion coefficient data as a function of temperature. This data is given for steel in Table 1. Table 1Coefficient of thermal expansion as a function of temperature. Temperature, T() FCoefficient of thermal expansion, (in/in/) F80 61047.640 61024.64061072.512061009.520061030.428061033.334061045.2(a)Is the rate of change of the coefficient of thermal expansion with respect to temperature more at F80Tthan at F340T? (b)The data given in Table 1 can be regressed to 22to get 211. Compare the results with part (a) if you used the regression curve to find the rate of change of the coefficient of thermal expansion with respect to temperature at F8010TaTaa10T961.2215106.2790106.0216TTand at F340. TSolution (a) Using the forward divided difference approximation method at F80T, TTTdTTdiii1)(80iT40TTTTii140408002.03.1
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