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`        derive relation between alpha,beta,gamma related to thermal expansion`
3 years ago

```							They are in the ratio of 1:2:3and hence can be written in one terms of another as:alpha = beta/2 = gamma/3.
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3 years ago
```							This is regarding linear , areal, volume expansion of substances.ΔL = α L ΔTArea 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 ΔTβ = ΔA/A  = 2 αVolume = V = L³Changed 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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2 years ago
```							Relation between alpha ad gammaV= L3L= L.[1+ alpha ∆T]v= L.3(1+alpha∆T)3Then, using binomial theorem(1+x)n = 1+nxTherefore, V= L.3(1+3alpha∆T)V= V.(1+3alpha∆T)V=3V.(1+Y∆T)Y=3alphaAlpha= Y/3Between alpha ad betaS= L2L=L.(1+B∆T)V= L.2(1+B∆T)2Again using binomial theorem (1+x)n=1+nxV= l.3(1+2B∆T)V=V.(1+2B∆T)V=V.(1+B∆t)B=2alphaAlpha = B/2Therefore,Alpha/1 =Beta(B)/2=Gamma(Y)/3Alpha:Beta:GammaHence solve...
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2 years ago
```							Mathematically, we can show that alpha, beta and gamma are related as follows: alpha :beta : gamma =1:2:3
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2 years ago
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