Question

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

Answer 1

It has given that the coefficient of apparent expansions of a liquid in two different vessels are a and b and the ratio of volume expansion of vessels is x : y.

To find : The real coefficient of expansion of liquid.

solution : let γ₁ be the coefficient of expansion of vessel 1

γ₂ be the coefficient of expansion of vessel 2.

and γ be the real coefficient of expansion of liquid.

given, γ - γ₁ = a ⇒γ₁ = γ - a and γ - γ₂ = b ⇒γ₂ = γ - b

so γ₁/γ₂ = (γ - a)/(γ - b) = x/y [ given ]

⇒y(γ - a) = x(γ - b)

⇒γy - ay = γx - bx

⇒γ(y - x) = (ay - bx)

⇒γ = (ay - bx)/(y - x)

Therefore the real coefficient of expansion of liquid is (ay - bx)/(y - x)