Two types of wall separate a refrigerated room from the rest of a building.Wall 1 has half the thermal conductivity of wall 2.Wall 2 is half as thick as wall 1.The two walls have the same area.The rate of heat flow through wall 2 compared with the rate of heat flow through wall 1 is
A)four times greater.
B)twice as great.
C)the same.
D)half as great.
E)one-quarter as great.

Question

Quizplus · Accepted Answer

The rate of heat flow through a wall is proportional to the thermal conductivity divided by the thickness. Let k1 and k2 be the thermal conductivity of wall 1 and wall 2, respectively, and let t1 and t2 be the thickness of wall 1 and wall 2, respectively. We know that k1 = 2k2 and t1 = 2t2, and the two walls have the same area. Therefore, the rate of heat flow through wall 1 is proportional to k1/t1 = 2k2/2t2 = k2/t2, and the rate of heat flow through wall 2 is proportional to k2/t2. Since k2/t2 is the same for both walls, the rate of heat flow through the two walls is the same.

Two Types of Wall Separate a Refrigerated Room from the Rest