A change in temperature of 100^oC causes a square plate to expand as shown in the figure. The coefficient of linear expansion of the plate is approximately

Question

Quizplus · Accepted Answer

From the diagram, we can see that the linear expansion is given by:
ΔL = LαΔT
where ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature.

Since the plate expands uniformly on all sides, we can say that:
ΔL = ΔW = LαΔT
where ΔW is the change in width.

Let S be the length of one side of the square plate. Then, we can say that:
S + ΔS = S + ΔL = S + LαΔT
where ΔS is the change in the side length.

Thus, we have:
ΔS/S = αΔT
or, α = ΔS/(SΔT)

From the diagram, we can see that ΔS = 0.5 cm, S = 10 cm, and ΔT = 100℃.

Substituting these values, we get:
α = 0.0005/℃

Therefore, the coefficient of linear expansion of the plate is approximately 0.0005/℃, which is given by choice C.

A Change in Temperature of 100oC Causes a Square Plate

A Change in Temperature of 100^oC Causes a Square Plate