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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 27C. When the temperature of the liquid is raised to 42C, the metal piece weighs 30.5 g. The density of the liquid at 42C 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 27C and Vθ at 42C. The density of the liquid at 27C is ρ0 = 1.24 × 103 kg/m3, and the density at 42C 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(42C27C) = 1.00104

or, α = 2.3 × 105/C


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