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L^3=gamma Show the dervation In thermal physis And relations between them

L^3=gamma
Show the dervation
In thermal physis And relations between them
 

Grade:11

1 Answers

Arun
25763 Points
2 years ago
This is regarding linear , areal, volume expansion of substances.
ΔL = α L ΔT
Area of a square sheet of dimensions L * L:
 = A+ΔA = (L+ α L ΔT)² = L² + 2 α L² ΔT   ignoring α² terms (too small).
ΔA = 2 α A ΔT
β = ΔA/A  = 2 α
Volume = V = L³
Changed volume = V+ ΔV = (L + α L ΔT)³
         = L³ + 3 α L³ ΔT  +  terms with α² or α³  ignored (too small)
ΔV = 3 α V ΔT
=>  gamma = ΔV/V = 3 α
 

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