Chapter 1, Problem 15P

The temperature distribution in a well-insulated axial rod varies linearly with respect to distance when the temperature at both ends is held constant as shown in Fig. P1.15. The temperature satisfies the equation of a line $T\left(x\right)=C_{1}x+C_2$, where C₁ and C₂, are constants of integration with units of °F/ft and °F, respectively

(a) Find the equation of the line T(x), and determine both constants C₁ and C₂

(b) Sketch the graph of the line T(x) for $0\le x\le 1.5$ ft, and clearly label C₁ and on your graph. Also, clearly indicate the temperature at the center of the rod ( $x=0.75$ ft).