The mass of a liter of milk is 1.032 kg. The butterfat that it contains has a density of 865 kg/m3 when pure, and it constitutes exactly 4.0 percent of the milk by volume. What is the density of the fat-free skimmed milk
1.01 kg/L
To find the density of the fat-free skimmed milk, we first need to calculate the mass of the butterfat in the milk.
Given that the mass of a liter of milk is 1.032 kg and the butterfat constitutes 4.0% of the milk by volume, we can calculate the mass of the butterfat as follows:
Mass of butterfat = Volume of milk x Density of butterfat
= 1 liter x 4.0% x 865 kg/m^3
To convert the volume of milk from liters to cubic meters, we need to divide by 1000 since there are 1000 liters in a cubic meter.
Volume of milk in cubic meters = 1 liter / 1000
Now, we can calculate the mass of the butterfat:
Mass of butterfat = (1 liter / 1000) x 4.0% x 865 kg/m^3
Next, we can find the mass of the fat-free skimmed milk by subtracting the mass of the butterfat from the mass of the whole milk:
Mass of fat-free skimmed milk = Mass of whole milk - Mass of butterfat
= 1.032 kg - Mass of butterfat
Finally, we can calculate the density of the fat-free skimmed milk by dividing the mass of the fat-free skimmed milk by its volume. Since we know that the volume of the fat-free skimmed milk is 1 liter, we can write:
Density of fat-free skimmed milk = Mass of fat-free skimmed milk / Volume of fat-free skimmed milk
= (1.032 kg - Mass of butterfat) / 1 liter
Plugging in the value of the mass of the butterfat, we can calculate the density of the fat-free skimmed milk.