In my lab of linear expansion, I need to find out the coefficient of linear expansion. The data I got for an aluminum rod are initial length is 59.7cm, the change in length is 95mm, the change in temperature is 75.4 Celsius degrees. I converted 59.7cm to 0.597m, and 95mm to 0.095m. But I got no where near the standard coefficient of linear expansion for aluminum, which is 22.5*10^-6, how come????????

Question

In my lab of linear expansion, I need to find out the coefficient of linear expansion. The data I got for an aluminum rod are initial length is 59.7cm, the change in length is 95mm, the change in temperature is 75.4 Celsius degrees. I converted 59.7cm to 0.597m, and 95mm to 0.095m. But I got no where near the standard coefficient of linear expansion for aluminum, which is 22.5*10^-6, how come????????

PLEASE HELP!!!!!!!THANKS A LOT!!!!!!!!!

Answer 1

Your length increase measurement was wrong by a wide margin. There is no way an aluminum bar's length will increase 16% due to a 75 degree C temperature change.

Are you sure the length change was not 95 micrometers? How did you measure it?

Answer 2

To find the coefficient of linear expansion, you need to use the formula:

ΔL = α * L * ΔT

Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the initial length
ΔT is the change in temperature

In your case, you have converted the initial length correctly to 0.597 m, and the change in length to 0.095 m.

Now, to find the coefficient of linear expansion, rearrange the formula to solve for α:

α = ΔL / (L * ΔT)

Substituting the values you have:

α = 0.095 m / (0.597 m * 75.4 °C)

Make sure that the change in temperature is in Kelvin, as the coefficient of linear expansion is typically given in per Kelvin.

To convert Celsius to Kelvin, you add 273.15:

α = 0.095 m / (0.597 m * (75.4 + 273.15) K)

α = 0.095 m / (0.597 m * 348.55 K)

Calculating this value, you should get a result close to 4.267 × 10^-5.

Now, it seems the value you obtained is not close to the standard coefficient of linear expansion for aluminum, which is 22.5 × 10^-6. Double-check your calculations and make sure you are using the correct values for the initial length, change in length, and change in temperature. Also, ensure that your units are consistent (for example, meters and Kelvin).

If you are getting a significantly different value, it could be due to errors in measurement or calculation. Make sure all measurements are accurate, and consider checking your calculations for any mistakes or misplaced decimal points.

If you are still having trouble obtaining the expected result, it might be useful to consult with your lab instructor or classmates to review the experiment setup and calculations to identify any potential errors.