Pressure is the measure of force acting on a unit area. Density is the measure of how closely any given entity is packed, or it is the ratio of the mass of the entity to its volume. The relation between pressure and density is direct. Change in pressure will be reflected in a change in density and vice-versa.

Pressure and Density

The pressure and density relationship for ideal gases and fluids is mathematically written as-

Pressure and Density Relationship

The pressure and density relation are direct. That is, the pressure is directly proportional to density. Which means that –

• When pressure increases, density increases.
• When the pressure decreases, density decreases.
• When density increases, pressure increases.
• When density decreases, the pressure decreases.

Pressure and Density Equation

Deriving pressure and density equations is very important to understand the concept. Below is the derivation of pressure and density relation for the ideal gas as well as for fluids.

Equation of State Ideal Gas

In thermodynamics, the relation between pressure and density is expressed through the equation of states for ideal gases. Consider an ideal gas with

• Pressure P
• Volume V
• Density ρ
• Temperature T
• Universal gas constant R
• Number of moles n

Applying Boyle’s law and Charles and Gay-Lussac law we get-

• Boyle’s law: For a given mass, at a constant temperature, the pressure times volume is constant. PV = C1
• Charles and Gay-Lussac law: For a given mass, at constant pressure, the volume is directly proportional to the temperature. V = C2T

Combining both we get-