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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? ​

1 Answer

3 votes

Answer:

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

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