Density Of Liquids:

The density of a liquid is defined in three ways: weight density, mass density, and particle density. The dissimilarity between these quantities may seem theoretically delicate, but in practical cases, the difference becomes obvious.

Mass density is defined in terms of the number of kilograms per meter cubed (kg/m³). The weight density is defined in newtons per meter cubed (N/m³) and is equivalent to the mass density multiplied by the acceleration in meters per second squared (m/s²) to which the sample is subjected. Particle density is stated as the number of moles of atoms per meter cubed (mol/m³), where 1 mol ≈ 6.02 x 10²³.

Let d_m be the mass density of a liquid sample (in kilograms per meter cubed), Assume d_w be the weight density (in newtons per meter cubed), and let d_p be the particle density (in moles per meter cubed). Let m symbolize the mass of the sample (in kilograms), let V symbolize the volume of the sample (in meters cubed), and let N symbolize the number of moles of atoms in the sample. Assume a be the acceleration (in meters per second squared) to which the sample is subjected. Then the equations below hold:

d_m = m/V

d_w = m_a/V

d_p = N/V

Another definition for weight density, mass density, and particle density use the liter, that is equivalent to a thousand centimeters cubed (1000 cm³) or one-thousandth of a meter cubed (0.001 m³), the standard unit of volume. Once you will see the centimeter cubed (cm³), also known as the milliliter as it is equivalent to 0.001 liter, used as the standard unit of volume.

These are basic definitions since they suppose that the density of the liquid is consistent throughout the sample.

PROBLEM:

A sample of liquid measures 0.275 m³. Its mass is 300 kg. What is its mass density in kilograms per meter cubed?

SOLUTION:

This is clear-cut as the input quantities are already given in SI. There is no requirement for us to convert from grams to kilograms, from milliliters to meters cubed, or whatever thing similar to that. We can merely divide the mass by the volume:

d_m = m/V

      = 300 kg/0.275 m³

      = 1090 kg/m³

We are entitled to go to three significant figures here as our input numbers are both given to three significant figures.