How Does Temperature Affect the Diameter of a Hole in an Aluminum Plate?

[Brit412]

Homework Statement

A hole in an aluminum plate has a diameter of 1.179 cm at 22.00 degrees Celsius.
Part A asks for the diameter of the hole at 199 degrees Celsius.?
Part B asks for the temperature of the hole when its diameter is 1.177 cm?

Homework Equations

∆L = alpha L(0) ∆T

The Attempt at a Solution

I got the answer for Part A.

Here's what I did so far for Part B:
I manipulated the equation as follows:
∆L/alpha*L(0) + Temp (initial) = Temp (final)

And I used the difference between 1.177 and 1.179 cm for ∆L, used 1.179 for L(0) and the 22 degrees C for the initial temperature. Is this method correct?

 

[praharmitra]

yes.

 

[thomate1]

I can confirm that your approach for Part B is correct. The equation you used, ∆L = alpha L(0) ∆T, is known as the thermal expansion equation and is commonly used to calculate the change in length of a material due to temperature change. In this case, you are trying to find the temperature at which the hole has a diameter of 1.177 cm, so your approach of using the difference in diameter (∆L) and the initial temperature (22 degrees C) is correct.

To solve for the final temperature, you would rearrange the equation as follows:

Temp (final) = ∆L/alpha*L(0) + Temp (initial)

Plugging in the values you provided, the final temperature would be approximately 199.2 degrees Celsius. This means that the hole would have a diameter of 1.177 cm at a temperature of 199.2 degrees Celsius.

Overall, your understanding and application of the thermal expansion equation is correct. Keep up the good work!