Question

1.1#33+34: A wire is attached between two objects that are being held at constant tem- peratures, 5C and 21C. We are concerned with the temperature of the wire at 3 points within: 1/4 way, 1/2 way, and 3/4 way. The temperature at each point is the average of the temperature of its neighbors. 5C 21 21C (a) Write down the system of equations (b) Solve the system of equations

Answer 1

The wire is attached to two objects hold at constant temperature 5 c and 21 c Given, the temperature at each point is average of temperature of its neighbours a) Temperature at x_1 is x_1 = x_2 + 5/2 2 x_1 - x_2 = 5 Temperature at x_2 is x_2 = x_1 + x_3/2 x_1 - 2 x_2 + x_3 = 0 temperature at x_3 is x_3 = x_2 + 21/2 - x_2 + 2 x_3 = 21 The system of equations are 2 x_1 - x_2 = 5 x_1 - 2 x_2 + x_3 = 0 - x_2 + 2 x_3 = 21 \r\n b) Solving this system of equations [2 1 0 -1 -2 -1 0 1 2] [x_1 x_2 x_3] = [5 0 21]