Reading X f mm Length Change L X f X i mm 74 0745 1217 0472 Copper

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

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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
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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.
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