Question

A metal rod is 25.000 cm long at 25.0 degrees Celsius. When heated to 102.0

Answer 1

Answer:

The coefficient of linear expansion $\alpha =2.8\times 10^-5$\°C

Explanation:

Given initial temperature $t_1=25$°C

And final temperature $t_2=102$°C

Initial length $l_1=25.000\ cm$

Final length $l_2=25.054\ cm$

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.

$l_2=l_1(1+\alpha (t_2-t_1))\\l_2-l_1=\alpha l_1(t_2-t_1)\\25.054-25.000=25.000(\alpha (102-25))\\0.054=\alpha\times 25(77)\\0.054=\alpha\times1925\\\alpha =\frac{0.054}{1925}=0.000028\C\\\alpha =2.8\times 10^-5$

So, $\alpha =2.8\times 10^-5$\°C