What is the Relationship Between Density and Pressure?

What-is-the-Relationship-Between-Density-and-Pressure

One of the Physics topics commonly practiced in school and your Physics tuition is the concept of density and pressure. Density and pressure have an integral relationship. The higher the density of an object that is exerting the pressure, the higher the pressure on the object on which the pressure is being exerted. It follows that the higher the pressure exerted on an object, the higher will be its density because the object will be compressed. This is especially true for liquids and gases.

Density

Density is defined as the mass per unit volume of an object. The object could be solid, liquid or gas. So, if you know the volume and mass of an object, you can calculate its density using the following equation:

Density = mass / volume

Or        r = m / v

The SI unit of density is kg/m3. For example, if the mass of an object is 20 kg and if it occupies a volume of 5 m3, then its density is 4 kg/m3.

The density (r) of an object depends on temperature and pressure. All substances expand to a certain degree as their temperature increases. Consequently, their density decreases. All substance compress to a greater or lesser degree as the pressure exerted on them increases. Consequently, their density increases.

You may be aware that the density of water is approximately 1,000 kg/m3 and the density of air is 1.3 kg/m3. But these are true only at normal temperature and pressure. At higher temperature, their densities become lower and at higher pressure, their densities become higher.

There is not much difference between the density of solid state and liquid state of most substances. For example, molten gold (at a high temperature) has almost the same density as solid gold (at normal temperature). This is because the molecules of the substance stay at approximately the same distance apart.

However, there is usually a huge difference in the density of liquid state and gaseous state of most substances. This is because the spacing between molecules in gaseous state is approximately 10 times the spacing between molecules in liquid state.

Pressure

Pressure is defined as the force per unit area (of the object on which the force is being exerted). Mathematically, it is expressed by the following equation:

P = F / A          Where, F is force and A is the area.

The SI unit of pressure is N/m2, which is also known as Pascal. So a pressure of 1 N/m2 is 1 Pascal.

It’s quite easy to calculate the pressure exerted by a solid object on another solid object, which is simply the first object’s weight in Newton (N) divided by the area (of contact) in square metres.

Calculating the pressure exerted by liquids and gases is not so straightforward. Since the molecules in liquid and gases are not tightly packed and move in a disordered motion, they exert pressure equally in all directions.

Thus, three factors come into play here: the depth the pressure is measured at (h), the density of the fluid (p) and the gravitational field strength. So the pressure of a liquid or gas is calculated using the following equation:

P = r * g * h

Where r is the density of the liquid or gas, g is the acceleration due to gravity, and h is the height (or depth) at which the pressure is measured. If you are having difficulty in grasping the topic, consider joining a Physics tuition class.