When a liquid in a glass vessel is heated, its apparent expansion coefficient is 10.30 × 10 - 4 ℃ - 1 . When the same liquid is heated in a metal vessel, its apparent expansion coefficient is 10.06 × 10 - 4 ℃ - 1 . If the coefficient of linear expansion of glass = 9 × 10 - 6 ℃ - 1 , what is the coefficient of linear expansion of metal?

Step-by-step solution

Here, γ ag = 10 .30 × 10 - 4 ℃ - 1 γ am = 10 .06 × 10 - 4 ℃ - 1 α g = 9 × 10 - 6 ℃ - 1 , α m = ? Now, γ r = γ ag + γ g = γ am + γ m ∴ 10 .30 × 10 - 4 + 3 × 9 × 10 - 6 = 10 .06 × 10 - 4 + γ m [ ∵ γ g = 3 × α a ] ∴ γ m = 10 .30 + 0 .27 - 10 .06 10 - 4 = 0 .51 × 10 - 4 α m = 1 3 γ m = 0 .51 × 10 - 4 3 = 0 . 17 × 10 - 4 = 17 × 10 - 6 ℃ - 1