Coefficient of apparent expansions of a liquid in two different vessels a and b. then the real coefficient of expansions of liquid, if the ratio of volume expansion of vessels is x : y

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)