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The graph of elongation of a rod of a substance A with temperature rise is shown in the first graph. A liquid B contained in a cylindrical vessel made out of substance A (graduated in millilitres) at 0 ° C is heated gradually. The readings of the liquid level in the vessel corresponding to different temperatures are shown in the second graph. The real coefficient of volume expansion of the liquid is

Options

  1. A2.7 × 1 0 - 5 ∘ C -1
  2. B15.4 × 1 0 - 5 ∘ C -1
  3. C16.2 × 1 0 - 5 ∘ C -1
  4. D151.2 × 1 0 - 5 ∘ C -1

Correct answer

C. 16.2 × 1 0 - 5 ∘ C -1

Step-by-step solution

From the graph (a), the slope of line is m = 1001.2 300 Δ L Δ T = 1001.2 - 1000.0 mm 3 0 0 - 0 ∘ C = 4 × 1 0 - 6 m ∘ C -1 But Δ L Δ T = L α ∴ α = 4 × 1 0 - 6 1 m = 4 × 1 0 - 6 ∘ C -1 As shown in graph (b), the slop of line is Δ V a Δ T = 1 0 0 3 - 1 0 0 0 mL 2 0 - 0 ∘ C = 3 2 0 mL ∘ C -1 But, Δ V a Δ T = V γ a ∴ γ a = 3 2 0 × 1 0 3 = 1 5 0 × 1 0 - 6 ∘ C -1 Since, γ a = γ r - γ c ∴ γ r = γ a + γ c = γ a + 3 α = 1 5 0 + 1 2 × 1 0 - 6 ∘ C -1 = 16.2 × 1 0 - 5 ∘ C -1

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