Answer to Question #106283 in Classical Mechanics for Jerico

Question

Data for experiment 105- Coefficient of Linear Expansion

Aluminum Rod

Initial Length = 70.20 cm
Initial Temperature = 22 degrees Celsius
Final Temperature- = 68 degrees Celsius
Final Length = 70.29 cm
Actual Value of Coefficient of Linear Expansion for Aluminum = 23.80 x10^-6 (degrees Celsius)^-1

Find the Following. Use the correct number of Significant Figures.

1. Experimental Value of Coefficient of Linear Expansion
2. Percentage Error

Answer 1

1. Experimental Value of Coefficient of Linear Expansion

Write the expression for the linear expansion:

$$\Delta L=\alpha L\Delta T,\\\space\\ \alpha=\frac{\Delta L}{L\Delta T}=\frac{70.29-70.20}{70.20\cdot(68-22)}=27.9\cdot10^{-5}\frac{1}{^\circ\text{C}}.$$

2. Percentage Error

$$\epsilon=\frac{|\alpha_a-\alpha|}{\alpha_a}\cdot100\%=\frac{|23.8-27.9|}{23.8}\cdot100\%=18\%.$$