Ideal Gas Law

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

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, lb)

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

p₁V₁/T₁ = p₂V₂/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

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