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

In steady one dimensional conduction through a single flat layer, the temperature gradient is constant along the thickness, so the temperature drop is shared out in direct proportion to distance.

Total rise across the wall = \(110 - 40 = 70\) degree C over a thickness of \(0.25\ m\), giving a gradient of \(\dfrac{70}{0.25} = 280\) degree C per metre.

Moving \(0.20\ m\) in from the inner face adds \(280 \times 0.20 = 56\) degree C to the inner temperature.

So the temperature at that point is \(40 + 56 = 96\) degree C. The thermal conductivity value given in the question does not change this answer, it only matters if you wanted to find the actual heat flow rate through the wall.

\[\boxed{T = 96 \text{ degree C}}\]