Consider two neighboring rectangular houses built from the same materials. One of the houses has twice the length, width, and height of the other. Under identical climatic conditions, what would be true about the rate that heat would have to be supplied to maintain the same inside temperature on a cold day? Compared to the small house, the larger house would need heat supplied at

Question

Quizplus · Accepted Answer

The rate at which heat needs to be supplied is proportional to the surface area through which heat is lost. Doubling each dimension of the house doubles the length and width of each face, so each face has 4 times the area, and since there are 6 faces (4 walls, a roof, and a floor), the overall effect is that the larger house has 4 times the surface area of the smaller house. However, the total increase in surface area does not mean the heat needs to be supplied at 6 times the rate because the increase in volume (and thus space to heat) is by a factor of 8 (2x length * 2x width * 2x height), but the rate of heat supply depends on the surface area through which heat is lost, not the volume. Therefore, the correct answer is that the larger house would need heat supplied at 4 times the rate of the smaller house to maintain the same inside temperature.

Consider Two Neighboring Rectangular Houses Built from the Same Materials