Chapter 1, Problem 16P

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 P1.16. The temperature satisfied the equation of a line. $T\left(x\right)=C_{1}x+C_2$ ., where C ₁ and C ₂ are constants of integration with units of °c/m and °C, respectively.

(a) Find the equation of the line T (x ), and determine both constants C ₁ and C ₂.

(b) Sketch the graph of the line T (x ) for $0\le x\le 0.5\text{ m}$, and clearly label C ₁ and C ₂ on your graph. Also, clearly indicate the temperature at the center of the rod ( $x=0.25$ )