Reading x f mm length change l x f x i mm 74 0745

Reading
X
f
(mm)
Length
Change
∆L = X
f
- X
i
(mm)
Steel 23 97 74 0.745 1.217 0.472
Copper 27 97 70 0.222 1.032 0.810
Aluminum 22 98 76 0.365 1.347 0.982
Calculations :
Steel Rod:
To find temperature change : ∆T = T
f
- T
i
so 97°C - 23°C = 74°C
To find length change : ∆L = X
f
- X
i
so 1.217mm - 0.745mm = 0.472mm
To find coefficient of linear expansion
: ∆L/(∆T*L₀) so 0.472mm / (74°C * 605mm) = 1.05e-5°C
Copper Rod:
To find temperature change : ∆T = T
f
- T
i
so 97°C - 27°C = 70°C
To find length change : ∆L = X
f
- X
i
so 1.032mm - 0.222mm = 0.810mm
To find coefficient of linear expansion
: ∆L/(∆T*L₀) so 0.810mm / (70°C * 605mm) = 1.91e-5 °C
Aluminum Rod:
To find temperature change : ∆T = T
f
- T
i
so 98°C - 22°C = °C
To find length change : ∆L = X
f
- X
i
so 1.347mm - 0.365mm = 0.982mm
To find coefficient of linear expansion
: ∆L/(∆T*L₀) so 0.982mm / (76°C * 605 mm) = 2.14e-5°C

Results :
Percent Difference =
| Experimental - Accepted Value | / (Accepted Value) * 100%
experimental value accepted value percent difference
steel 0.000010543 0.000013 18.9%
copper 0.000019126 0.000017 12.5%
aluminum 0.000021357 0.000024 11.0%
Discussion :
The values for the coefficients of linear expansion for steel, copper, and aluminum found
experimentally are close to, but do not agree with the accepted values. The percent differences
from the accepted values of the coefficients of linear expansion are outlined in the table above.
Steel has the largest percent difference while aluminum has the smallest percent difference.
Some possible sources of this discrepancy in the experimental values versus the accepted values
could likely be caused by human error. For example, using the meter stick to measure lengths to
the nearest mm was difficult. The gauge was also difficult to use and the materials inside the
device could have absorbed some of the heat.
In conclusion, the increase in a linear ∆L is proportional to the increase in
temperature and the initial linear dimension.