Question

A litre of whole milk has a mass of 1032 g. It contains 4% butterfat by volume. The
specific gravity of butterfat is 0.865 g/cc. What is the density in g/cc of the fat free
“skimmed-milk”?

Answer 1

A liter of whole milk has a mass of 1032 g. It contains 4% butterfat by volume. The specific gravity of butterfat is 0.865 g/cc. What is the density in g/cc of the fat free "skimmed-milk"?

$$1 \text{ liter} = 1000 \text{ cm}^3$$

Whole milk contains 4% butterfat by volume, therefore volume of butterfat equals:

$$V_b = 0.04 * 1000 \text{ cm}^3 = 40 \text{ cm}^3$$

And its mass:

$$m_b = V_b * \rho_b = 40 \text{ cm}^3 * 0.865 \frac{g}{\text{cm}^3} = 34.6 \text{ g}$$

Therefore, mass of pure milk in whole milk equals:

$$m_m = 1032 \text{ g} - 34.6 \text{ g} = 997.4 \text{ g}$$

And its volume:

$$V_m = 1000 \text{ cm}^3 - 4 \text{ cm}^3 = 960 \text{ cm}^3$$

Therefore, density of the fat free milk equals:

$$\rho = \frac{m_m}{V_m} = \frac{997.4 \text{ g}}{960 \text{ cm}^3} = 1.039 \frac{g}{\text{cm}^3}$$

Answer: $1.039 \frac{g}{\text{cm}^3}$