Using similar techniques that were originally developed to process miniaturized semiconductor electronics,scientists and engineers are creating Micro-Electro-Mechanical Systems (MEMS).Consider a silicon post that is part of a MEMS device that is being heated by an electric current flowing through the post.The coefficient of thermal expansion for silicon is 3.2 * 10^-6 K^-1.The post is 1950 $\mu$m tall and 45 $\mu$m in diameter at room temperature.At any given time,you may assume that the temperature is constant along the entire length of the post,which strictly speaking is not the case.As the post heats up from room temperature to 492^oC,its height will be A)1950 $\mu$m. B)1953 $\mu$m. C)1947 $\mu$m. D)1956 $\mu$m. E)1944 $\mu$m.

Question

Quizplus · Accepted Answer

The formula to calculate the change in height due to the change in temperature is:

Δh = hαΔT

Where:

h = height of the post = 1950 μm
α = coefficient of thermal expansion = 3.2 × 10^-6 K^-1
ΔT = change in temperature = 492°C - room temperature

Converting the temperature from Celsius to Kelvin:

ΔT = (492 + 273) K - 273 K = 492 K

Substituting the values:

Δh = 1950 μm × 3.2 × 10^-6 K^-1 × 492 K = 3.21216 μm

Therefore, the total height of the post at 492°C would be:

1950 μm + 3.21216 μm = 1953.212 μm ≈ 1953 μm

So the best choice is B) 1953 μm.

Using Similar Techniques That Were Originally Developed to Process Miniaturized μ\muμ

Using Similar Techniques That Were Originally Developed to Process Miniaturized $\mu$