Respuesta :
The coefficient of aerial expansion for metal b is one-fourth of the coefficient of aerial expansion for metal a.
Note: Most probably your question was to find the relation between the coefficient of aerial expansion for metal a and metal b.
Coefficient of linear expansion:
The ratio of the change in length of a solid to its original length when there is a unit change in temperature at constant pressure is called the coefficient of linear expansion. It is given by the formula,
α=ΔL/(Lo*ΔT)
where α is the coefficient of linear expansion, ΔL is the change in length Lo is the original length, and ΔT is the change in temperature.
Coefficient of aerial expansion:
The ratio of the change in surface area of a solid to its original surface area when there is a unit change in temperature at constant pressure is called the coefficient of aerial expansion. It is given by the formula,
β=ΔA/(Ao*ΔT)
where β is the coefficient of aerial expansion, ΔA is the change in surface area, Ao is the original surface area, and ΔT is the change in temperature.
Relation between α and β:
The relation between the coefficient of linear expansion and aerial expansion is given by the formula,
β=2α
Given that metal a has a coefficient of linear expansion four times that of metal b. It can be written.
α₁=4α₂
where α₁ is the coefficient of linear expansion for metal a and α₂ is the coefficient of linear expansion for metal b.
Then from the above relation, the ratio of the coefficient of aerial expansion β₁ and β₂ for metal a and metal b respectively is,
β₁/ β₂ = 2*(α₁)÷(2*(α₂))
β₁/ β₂= 2*(4α₂)÷(2*(α₂))
β₁/ β₂=4
β₂= β₁/4
Therefore, the coefficient of areal expansion of metal b is one-fourth of the coefficient of aerial expansion of metal a.
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