Question

what is the relation between coefficient of apparent and real expansion of liquids.

Answer 1

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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+Ag
Ag=3*Lg(coefficient of linear expansion)

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Answer 2

coefficient means in lower tempretures also when they expand.
real means at normal tempreture