Physics. Repeat Problem 1 for the CTE of copper (column 3 of Table 1).
Problem 1
Physics. The coefficient of thermal expansion (CTE) is a measure of the expansion of an object subjected to extreme temperatures. To model this coefficient, we use a Michaelis–Menten function of the form
where C = CTE, T is temperature in K (degrees Kelvin), and Cmax and M are constants. Table 1† lists the coefficients of thermal expansion for nickel and for copper at various temperatures.
Table 1 Coefficients of thermal expansion
T (K) | Nickel | Copper |
100 | 6.6 | 10.3 |
200 | 11.3 | 15.2 |
293 | 13.4 | 16.5 |
500 | 15.3 | 18.3 |
800 | 16.8 | 20.3 |
1,100 | 17.8 | 23.7 |
†National Physical Laboratory
(A) Plot the points in columns 1 and 2 of Table 1 on graph paper and estimate Cmax to the nearest integer. To estimate M, add the horizontal line to your graph, connect successive points on the graph with straight-line segments, and estimate the value of T (to the nearest multiple of fifty) that satisfies .
(B) Use the constants and M from part (A) to form a Michaelis–Menten function for the CTE of nickel.
(C) Use the function from part (B) to estimate the CTE of nickel at 600 K and to estimate the temperature when the CTE of nickel is 12.
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