The temperature distribution in a well-insulated axial rod shown in figure 1.23

Question

The temperature distribution in a well-insulated axial rod shown in figure 1.23 varies linearly with respect to distance when the temperature at both end is held constant. The temperature satisfies the equation T(x)=Cl x+C2, where Cl and C2 are constants of integration with units of degree F= f t and degree F, respectively. The temperatures at two points of the rod are measured and are given in Table 1.16. Determine constants, Cl and C2, and write the equation of line T(x). Sketch the graph of the line T(x) for 0 = t = 1.5 ft, and clearly indicate Cl and C2 on your graph. Also, clearly indicate the temperature at the center of the rod (x = 0.75). T(x) = Clx +C2, where Cl and C2 are integration with units of degree F/ft and degree F, respectively. Determine both constants. Cl and C2, and write the equation of the line T(x). (10 b) Sketch the graph of the line T(x) for 0 = t =1.5 ft, and clearly indicate C Figure 1.23: Well-insulated coaxial rod. Table 1.16: Temperature of the rod at two different locations. Figure 1.23

Explanation / Answer

these two questions look identical..
use T=30 at x=0 in the T(x) equation to get 30=C1(0)+C2 and solve for C2=30, use T=70 at x=1.5 and C2=30 in the T(x) equation to get 70=C1(1.5)+30 and solve for C1=26.67. so your equation is T(x)=26.67x+30.

the above graph is the plot. your line shoud start at (0,30), has a slope of 26.67 and end at (1.5,70). the temperature at the center of rod is x==.75, y=50

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