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A metal piece weighs 46 g in air and 30 g when immersed in a liquid of density 1.24e3 kg/m³ at 27 deg C. When the liquid is heated to 42 deg C, the same piece weighs 30.5 g, and the liquid density falls to 1.20e3 kg/m³. Calculate the coefficient of linear expansion of the metal.

1. 1.8e-5 per deg C
2. 2.3e-5 per deg C
3. 2.8e-5 per deg C
4. 3.0e-5 per deg C

Correct answer: 2.3e-5 per deg C

Solution

At 27 C: loss = 46-30 = 16 g, so 16 = rho1*V1 (in consistent units). At 42 C: loss = 46-30.5 = 15.5 g, so 15.5 = rho2*V2 with V2 = V1*(1+3*alpha*15). Dividing: 16/15.5 = (rho1*V1)/(rho2*V2) = (1.24/1.20)/(1+3*alpha*15). Solving gives 1+45*alpha = (15.5/16)*(1.24/1.20) = 0.96875*1.03333 = 1.00104, so 45*alpha = 0.00104, alpha ~ 2.3e-5 per deg C.

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