Answer:
The coefficient of linear expansion [tex]\alpha =2.8\times 10^-5[/tex]\°C
Explanation:
Given initial temperature [tex]t_1=25[/tex]°C
And final temperature [tex]t_2=102[/tex]°C
Initial length [tex]l_1=25.000\ cm[/tex]
Final length [tex]l_2=25.054\ cm[/tex]
We have to find the coefficient of linear expansion
The coefficient of linear expansion is defined as the change in length per unit original length divide by the change in temperature.
[tex]l_2=l_1(1+\alpha (t_2-t_1))\\l_2-l_1=\alpha l_1(t_2-t_1)\\25.054-25.000=25.000(\alpha (102-25))\\0.054=\alpha\times 25(77)\\0.054=\alpha\times1925\\\alpha =\frac{0.054}{1925}=0.000028\C\\\alpha =2.8\times 10^-5[/tex]
So, [tex]\alpha =2.8\times 10^-5[/tex]\°C
