relationship between alpha beta and gama
Answers
Explanation:
in Thermal Expansion. As the temperature increases, the volume of the material also increases. This is known as thermal expansion. It can also be explained as the fractional change in the length or volume per unit change in the temperature.
Answer:-
We know that,
L =L• (1+αΔT)
α= coefficient of linear expansion
And,
A= A• (1+βΔT)
β= coefficient of aerial expansion
And,
And,
V= V•(1+γΔT)
γ= coefficient of cubical expansion.
So, now
V= V• + γV•ΔT
V= V•(1+γΔT)
L³= L•³ (1+αΔT)³
L³= L•³(1+3αΔT + 3α²ΔT² +α³ΔT³)
L³= L•³(1+3αΔT)
{Neglecting 3α²ΔT² and α³ΔT³ because they are very smaller than 1}
L³= L•³(1+3αΔT)
V= L•³(1+3αΔT)
V•(1+γΔT) = V•(1+3αΔT)
1+γΔT = 1+3αΔT
γΔT = 3αΔT
γ=3α
And β=2α
A= A•(1+βΔT)
L²= L•²(1+αΔT)²
A= L•²(1+2αΔT+α²ΔT²)
A= A•(1+2αΔT)
A•(1+βΔT) = A•(1+2αΔT)
{α²ΔT² Neglecting them due to very smaller volume}
β=2α
α:β:γ=1:2:3
hope it will help you....