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Question

# A piece of metal weighs 46 g in air and 30 g in a liquid of density 1.24 × 103kg/m3 kept at 27∘C. When the temperature of the liquid is raised to 42∘C, the metal piece weighs 30.5 g. The density of the liquid at 42∘C is 1.20 × 103kg/m3. Calculate the coefficient of linear expansion of the metal.

A

2.3 × 106/°C

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B

1.2 × 10-5/°C

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C

1.2 × 105/°C

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D

2.3 × 10-5/°C

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Solution

## The correct option is D 2.3 × 10-5/°C Let the volume of the metal piece be V0 at 27∘C and Vθ at 42∘C. The density of the liquid at 27∘C is ρ0 = 1.24 × 103 kg/m3, and the density at 42∘C is ρθ = 1.20 × 103 kg/m3. The weight of the liquid displaced = apparent loss in the weight of the metal piece when dipped in the liquid. Thus, v0ρ0 = 46 g - 30 g = 16 g and vθρθ = 46 g - 30.5 g = 15.5 g. Thus, vθv0 = ρ0ρθ × 15.516 or, 1+3αΔθ = 1.24 × 103 15.51.20 × 103 × 16 or, 1+3θ(42∘C−27∘C) = 1.00104 or, α = 2.3 × 10−5/∘C

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