The coefficient of linear expansion measures how much a material expands or contracts in length when its temperature changes. The coefficient of areal expansion, on the other hand, measures how much a material expands or contracts in area when its temperature changes.
To relate the coefficients of linear expansion to the coefficient of areal expansion, we need to consider the relationship between length and area.
Let's denote the coefficient of linear expansion for metal A as αA and the coefficient of linear expansion for metal B as αB. The coefficient of areal expansion for metal A, denoted as βA, is related to αA by the equation:
βA = 2αA
Similarly, the coefficient of areal expansion for metal B, denoted as βB, is related to αB by the equation:
βB = 2αB
Therefore, if the coefficient of linear expansion of metal A is three times the coefficient of linear expansion of metal B (αA = 3αB), we can determine their respective coefficients of areal expansion as:
βA = 2(3αB) = 6αB βB = 2αB
In this case, the coefficient of areal expansion for metal A (βA) is six times the coefficient of areal expansion for metal B (βB).