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The coefficient of real expansion equals the sum of coeffiient of apparent expansion and the coefficient of expansion of vessel.(all being volume expansion)
Aᵣ = Aₐ + Aᵥ
Two equations formed are
Aᵣ = C + ¥c, and
Aᵣ = S + ¥s ( since real expansion of liquid is same in both cases)
Equating the R.H.S. of the two equations, we get
¥s = C + ¥c - S
We know,
linear expansion = 1/3 (volumetric expansion)
=> linear expansion = 1/3 (¥s)
=> linear expansion = 1/3 (C + ¥c - S)
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