Question

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

degrees Celsius, it is 25.054 cm long. What is the coefficient of linear expansion
for this metal? ​

Answer 1

The coefficient of linear expansion
`\alpha =2.8* 10^-5`\°C

Step-by-step 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* 25(77)\\0.054=\alpha*1925\\\alpha =(0.054)/(1925)=0.000028\C\\\alpha =2.8* 10^-5`

So,
`\alpha =2.8* 10^-5`\°C