Derive relation between alpha,beta and gamma? that is alpha=beeta/2=gamma/3.but i need derivation.
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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
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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Answer:
compare the equTion
u will get the answer
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