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Question: If 5 litres of kerosene have a mass of 5 kg, then what is the density of kerosene?...

If 5 litres of kerosene have a mass of 5 kg, then what is the density of kerosene?

Explanation

Solution

To answer this question, it is important to understand the definition of density and its relationship with the quantities mass and volume. Also, it is important to express the units of density in the units of the terms mass and volume given in the question.

Complete step-by-step solution:
If a body has a mass M, it is the sum of the individual masses of the particles that form the body. The total mass M, of the body indicates the total mass of the body but it does not indicate how the mass is distributed.
The distribution of mass in the body matters because, even if equal masses of an iron block and cotton ball is taken, lifting the iron block requires more effort compared to the ball of cotton of the same mass.
This distribution of the mass is represented by a quantity called density. The density represents how the mass is spread across the entire volume of the body.
Mathematically, the density is defined as the total mass divided by the volume of the body.
Density, D=MVD = \dfrac{M}{V}
The SI unit of mass and volume are kg and m3{m^3} respectively. Therefore, the SI unit of density is given by – kgm3\dfrac{{kg}}{{{m^3}}}
Given,
The unit of volume is litres and the unit of mass is in kg.
Mass, M = 5 kg Volume, V = 5 litres
Since the volume is given in litres, we have to convert to m3{m^3} as it is the SI unit.
The relationship between litre and m3{m^3} is given by –
1l=10−3m31l = {10^{ - 3}}{m^3}
Therefore, volume, V = 5 litres = 5×103m35 \times {10^3}{m^3}
Substituting we get –

Density, D=MV=55×10−3=1000kgm−3D = \dfrac{M}{V} = \dfrac{5}{{5 \times {{10}^{ - 3}}}} = 1000kg{m^{ - 3}}
Hence, the density of kerosene is 1000kgm31000\dfrac{{kg}}{{{m^3}}}

Note: If the values of mass and the volume in litres are the same, it can only be possible for one substance, which is water, since the density of water is 1000kgm−31000kg{m^{ - 3}}. No other fluid or substance other than water can have the magnitudes of mass and the volume in litres, same in number. This is also why one litre of water is equally considered as one kilogram of water.