In perfect or ideal gas the change in density is directly related to the change of temperature and pressure as expressed by the Ideal Gas Law.

The Ideal Gas Law and the Individual Gas Constant - R

The Ideal Gas Law relates pressure, temperature, and volume of an ideal or perfect gas. The Ideal Gas Law can be expressed with the Individual Gas Constant:

p · V = m · R · T         (1)
where
p = absolute pressure (N/m², lb/ft²)
V = volume (m^3, ft³)
m = mass (kg, slugs)
R = individual gas constant (J/kg.^oK, ft.lb/slugs.^oR)
T = absolute temperature (^oK, ^oR)

This equation (1) can be modified to:

p = ρ · R · T         (2)
where the density
ρ = m / V         (3)

The Individual Gas Constant - R - depends on the particular gas and is related to the molecular weight of the gas.
Equation (1) can also be modified to

p₁ V₁ / T₁ = p_{2 ·} V₂ / T₂         (4)

expressing the relationship between different states for a given mass of gas.

The Ideal Gas Law and the Universal Gas Constant - R_u

The Universal Gas Constant is independent of the particular gas and is the same for all "perfect" gases. The Ideal Gas Law can be expressed with the Universal Gas Constant:

p · V = n · R_u· T         (5)
where
p = absolute pressure (N/m², lb/ft²)
V = volume (m^3, ft³)
n = is the number of moles of gas present
R_u = universal gas constant (J/mol.^oK, lbf.ft/(lbmol.^oR))
T = absolute temperature (^oK, ^oR)

Example - The Ideal Gas Law

A tank with volume of 1 ft³ is filled with air compressed to a gauge pressure of 50 psi. The temperature in tank is 70 ^oF.
The air density can be calculated with a transformation of the ideal gas law (2) to:

ρ= p / (R · T)         (6)
ρ= [(50 (lb/in²) + 14.7 (lb/in²)) · 144 (in²/ft²)] / [1716 (ft.lb/slug.^oR)· (70 + 460) (^oR)]
    = 0.0102 (slugs/ft³)

The weight of the air is the product of specific weight and the air volume. It can be calculated as:

w = ρ · g · V         (7)
w = 0.0102 (slugs/ft³) · 32.2 (ft/s²) · 1 (ft³)
    = 0.32844 (slugs.ft/s²)
    = 0.32844 (lb)

Note!

The Ideal Gas Law is accurate only at relatively low pressures and high temperatures. To account for the deviation from the ideal situation, another factor is included. It is called the Gas Compressibility Factor, or Z-factor. This correction factor is dependent on pressure and temperature for each gas considered.
The True Gas Law, or the Non-Ideal Gas Law, becomes: