the coefficient of area expansion of metal A is also 3 times that of metal B
Explanation:
When a material is heated, the lenght of the material increases by the following amount:
[tex]L=(1+\alpha \Delta T)L_0[/tex]
where
[tex]\alpha[/tex] is the coefficient of linear expansion of the material
[tex]L_0[/tex] is the initial length
[tex]\Delta T[/tex] is the increase in temperature
The area of the material is proportional to the square of the length, this means that the expansion in area is proportional to the square of the increase in length:
[tex]\Delta A \propto \Delta L^2[/tex]
Which means that the coefficient of expansion for the area is
[tex]\alpha_A = (1+\alpha)^2 = 1 + 2\alpha +O(\alpha)[/tex]
Therefore, the coefficient of area expansion is twice that of linear expansion.
In this problem, the coefficient of linear expansion of metal A is 3 times that of metal B:
[tex]\alpha_A = 3 \alpha_B[/tex]
Therefore, this means that the coefficient of area expansion of metal A is also 3 times that of metal B, since the two coefficients are directly proportional to each other.
Learn more about temperature:
brainly.com/question/1603430
brainly.com/question/4370740
#LearnwithBrainly
