Question

A concrete wall is insulated on one side and exposed to ambient air at 25 C on the other. If the air is constant and there is no heat generation in the wall, after an extended period of time, which of the following shows the temperature distribution?

A) Uniform temperature distribution throughout the wall, with a temperature equal to the average of the ambient air and the insulated side.
B) Linear temperature gradient from the insulated side (higher temperature) to the exposed side (ambient air temperature).
C) Temperature increasing exponentially from the insulated side to the exposed side.
D) Non-linear temperature distribution with random fluctuations due to air movement.

Answer 1

The temperature distribution in an insulated, concrete wall exposed to ambient air will be a linear temperature gradient, with higher temperature on the insulated side and the exposed side at ambient temperature.

Step-by-step explanation:

The temperature distribution in a concrete wall that is insulated on one side and exposed to ambient air will not be uniform or exponential. After an extended period of time, the distribution will be a linear temperature gradient from the insulated side, which will have a higher temperature, to the exposed side, which is at ambient air temperature. This occurs because heat is conducted through the wall at a rate consistent with the materials' thermal conductivities, resulting in a steady state where heat transfer is steady and no further change in the temperature distribution occurs. The insulated side will slow down the heat loss, leading to a higher temperature than the ambient, while the exposed side will match the ambient air temperature due to ongoing heat exchange with the environment.