Question

A red brick wall of length 5 m, height 4 m and thickness 0.25 m has a temperature on the inner surface of 40 degree C and on the outer surface of 110 degree C. The thermal conductivity of the red brick is k = 0.70 W/mK. What will be the temperature at an interior point of the wall, 20 cm from the inner wall?

• A. 96 degree C
• B. 74 degree C
• C. 54 degree C
• D. 48 degree C

Hint:

Think of the temperature as changing in a straight line from the inner face to the outer face, then find its value at 20 cm.

Answer 1

The Correct Option is A

Step 1: This is steady state, one-dimensional conduction through a flat brick wall with no heat generation inside the wall. Under these conditions the temperature does not curve, it changes in a straight line from one face to the other, no matter what the value of k is.

Step 2: Take x as distance measured from the inner face. At x = 0, T = 40 degree C. At x = L = 0.25 m, T = 110 degree C. Since the profile is linear, we can write \(T(x) = T_{inner} + (T_{outer} - T_{inner}) \times \dfrac{x}{L}\).

Step 3: Put in the numbers for x = 0.20 m: \(T(0.2) = 40 + (110-40) \times \dfrac{0.2}{0.25} = 40 + 70 \times 0.8 = 40 + 56 = 96 \text{ degree C}\).

Step 4: As a check, work out the heat flux first. \(q = \dfrac{kA\Delta T}{L} = \dfrac{0.70 \times (5 \times 4) \times 70}{0.25} = 3920\ W\). The temperature at 0.2 m from the inner face is then \(T = 40 + \dfrac{q \times x}{kA} = 40 + \dfrac{3920 \times 0.2}{0.70 \times 20} = 40 + 56 = 96 \text{ degree C}\). Both methods agree, so the wall area and k value only confirm the linear result, they do not change it.

Step 5: 74 degree C, 54 degree C and 48 degree C come from taking the wrong fraction of the temperature rise (for example measuring from the wrong face, or dividing by the wrong length), so they are incorrect. The correct temperature is 96 degree C.