The density The mass of a substance is the quotient between the mass of the sample and the volume it occupies, its unit of measurement being kg / m3 in the International System of Units. The Greek letter ρ (rho) is often used to denote it.
The density of water, which is the universal fluid, is 1000 kg / m3 or 1 g / cm3 at 25 ºC, since the density undergoes changes with temperature and pressure.
Objects with the same dimensions are often found, and yet some are lighter and others are heavier, this is due to differences in density. The lightest object has a lower density than the heaviest.
Density is an intensive property of matter, which does not depend on the amount of mass of the sample being examined, since it is the mass / volume ratio that remains constant for the same substance. This makes it possible to differentiate one substance from another.
Materials have a wide range of densities, the lowest are those of gases, so the unit kg / m3 it is very large and grams / liter or g / L is preferred. Other frequently used units are grams / milliliter or grams / cubic centimeter.
The concept of density is especially useful when working with continuous media such as fluids, whether they are gases or liquids.
According to the definition given, the density has a mathematical formula given by:
Where density is ρ, m is mass and V is volume.
The density of an object can be calculated if its mass and volume are previously measured. The latter is not always easy, as the sample can be irregular, however there are several methods.
If the sample has a regular geometric shape, there are formulas that allow the volume to be calculated based on its dimensions. As for the mass, this can be obtained with the help of a balance.
If the object is not regular, its volume can be determined by measuring the volume displaced by completely submerging it in a fluid such as water..
For this, a graduated container is used and it is filled with an exact volume of water V1, then the object is completely submerged and the new volume V is measuredtwo. The volume of the object equals the difference Vtwo - V1.
To use this method, the sample substance must not dissolve in the water and a graduated container of the appropriate size must be available..
Archimedes' principle can be used to find the density of a solid sample. The principle states that a body partially or totally submerged in a fluid experiences an upward force called thrust, the magnitude of which is equal to the weight of the fluid displaced by placing the body.
To determine the density of an object using Archimedes' principle, the following steps are followed:
Determine the mass mc of the object using a scale.
Fill a container with a fluid whose density is known, which is usually distilled water. This value is called m1.
Completely submerge the solid object in the container with water, taking care that it does not touch the walls. It is observed that the fluid exerts a thrust AND on the solid upwards, and this in turn, by Newton's third law, exerts a reaction of equal magnitude on the water, but in the opposite direction.
When weighing the set, the value obtained, called mtwo, will be that of the container filled with water plus this reaction.
From the equation for density, we can express the volume V of the body, which is equal to the volume of fluid displaced:
The mass of the dislodged fluid mF It is simply:
mF = mtwo −m1
Therefore:
It is the density as defined above: the ratio of the mass to the volume of the sample.
Call also specific gravity, It is the density of one substance with respect to another that is taken as a reference. For solids and liquids this reference substance is water at 4ºC and 1 atm of pressure and for gases it is dry air. It is calculated by:
Relative density = density of material / density of water
Both the density of the material and that of water must be measured under the same conditions of pressure and temperature, and expressed in the same units..
The following image shows the relative densities of steel and wood.
Since the density of steel is 7800 kg / m3 and that of water is 1000 kg / m3, The relative density of steel, denoted as sg, is:
sg = 7800/1000 = 7.8
For its part, the relative density of wood is:
sg = 500/1000 = 0.5
Objects whose relative density is less than 1 float in water, while those whose relative density is greater than 1 sink.
It is calculated by the quotient between the mass of the sample and its volume, including pores and spaces with air:
Apparent density = Mass / Volume = (Mass particles + Mass air )/ (Volume particles+ Volume air)
Calculate the density of the cork, knowing that a cube made with this material, which measures 1.5 cm on a side, has a mass of 1 g.
The volume of a cube is:
V = ℓ3 = (1.5 cm)3 = 3.375 cm3
The statement indicates that the mass m of the cube is m = 1 g, therefore, substituting values in the density equation:
ρ = m / V = 1g / 3.375 cm3 = 0.296 g / cm3
What is the mass of a sphere made of osmium of radius 15 cm?
Starting from the density equation:
The mass is cleared as:
m = ρ ∙ V
It is necessary to calculate the volume of the sphere, which is given by the formula:
Where r is the radius of the sphere. Since the density of osmium is 22570 kg / m3, It is convenient to express the 15 cm in meters:
r = 15 cm = 15 × 10−2 m
V = (4/3) π × (15 × 10−2 m)3 = 0.01414 m3
This value is substituted in the clearance for the mass:
m = ρ ∙ V = 22570 kg / m3 × 0.01414 m3 = 319.1 kg
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