Question

the apparent coefficient of expansion of a liquid when heated in a brass vessel is X and when heated in a tin vessel is Y. If alpha is the coefficient of linear expansion for brass the coefficient of linear expansion of tin is ?

Answer 1

• If α is the coefficient of linear expansion for brass then the coefficient of linear expansion of tin is Y - X + 3α / 3.

Given-

• Apparent coefficient of expansion of a liquid when heated in brass vessel is X.
• And when heated in a tin vessel is Y
• Coefficient of linear expansion of brass = α

Let the volume expansion of liquid be δ and linear expansion of tin be αt

So,

X = 3 α + δ -------(i)

Y = 3 αt + δ --------(ii)

From equation (i) and (ii) we get

δ = X - 3α and

Y = 3 αt + X - 3α or

αt = $\frac{Y-X+3a}{3}$

Regards