what is the relation between alpha a and alpha l in the chapter of thermal expansion
Answers
Answer:
The relation between alpha, beta, and gamma is given in the form of a ratio and the ratio is 1:2:3 and can be expressed as:
alpha=fracbeta2=fracgamma3
Following is the relation between the three:
L = L (1 + α.ΔT)
Where, α is the coefficient of linear expansion
A = A (1 + β.ΔT)
Where, β is the coefficient of aerial expansion
V = V (1 + γ.ΔT)
Where, γ is the coefficient of cubical expansion
V = V + γV.ΔT
V = V (1 + γ.ΔT)
L3 = L3 (1 + α.ΔT)3
L3 = L3 (1 + 3α.ΔT + 3α2.ΔT2 + α3.ΔT3)
L3 = L3 (1 + 3α.ΔT)
Since 3α2.ΔT2 and α3.ΔT3 are smaller than 1, we are not considering them.
L3 = L3 (1 + 3α.ΔT)
V = L3 (1 + 3α.ΔT)
V (1 + γ.ΔT) = V (1 + 3α.ΔT)
1 + γ.ΔT = 1 + 3α.ΔT
γ.ΔT = 3α.ΔT
γ = 3α
β = 2α
A = A (1 + β.ΔT)
L2 = L2 (1 + α.ΔT)2
A = L2 (1 + 2α.ΔT + α2.ΔT2)
A = A (1 + 2α.ΔT)
A (1 + β.ΔT) = A (1+ 2α.ΔT)
Since α2.ΔT2 has a smaller volume, it is not considered
β = 2α
α : β : γ = 1 : 2 : 3
I HOPE ITS HELPFULL ...
Answer:
The relationship between the area and linear thermal expansion coefficient is given as the following: αA=2αL α A = 2 α L .
Hey mate here is your answer