Problem Solving

3. A wall is 15cm thick. At the outside surface, the temperature is 3C and at the inside surface, it is 23C. If the temperature changes at a constant rate through the wall, write an equation for the temperature T in the wall in terms of the distance x from the outside surface to the inside surface.

Solution:

This will be a linear equation, so the form will be T = mx + b. Now all we need is to find the slope m and the y intercept b. Let’s look at the data given…

When x = 0, T = 3C and when x = 15, T = 23C.

Now we have two data points: (0, 3) and (15, 23). To get the slope,

m = (23-3)/(15-0) = 1.333

Then T = 1.333x + b. Now plug one of the data points into this equation to get b.

3 = 1.333(0) + b b = 3

So…. T = 1.333x + 3