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 (m3, 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 = p2 V2 / T2         (4)

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

The Ideal Gas Law and the Universal Gas Constant - Ru

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 Ru T  

  = N k T       (5)

where

p = absolute pressure (N/m2, lb/ft2)

V = volume (m3, ft3)

n = is the number of moles of the gas present

Ru = universal gas constant (J/mol.oK, lbf.ft/(lbmol.oR) = 8.3145 J/mol K

T = absolute temperature (oK, oR)

N = number of molecules

k = Boltzmann constant = 1.38066 10-23 J/K = 8.617385 10-5 eV/K

  • One mole of an ideal gas at STP occupies 22.4 liters.

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 oR)+ (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:

P V = Z n R T  (7)

where

Z = Gas Compressibility Factor

n = number of moles of gas present

Related Topics

  • Air Psychrometrics - The study of moist and humid air - air condition - psychrometric charts, Mollier diagrams, air temperature, absolute and relative humidity, moisture content and more
  • Fluid Mechanics - The study of fluids - liquids and gases. Involves various properties of the fluid, such as velocity, pressure, density and temperature, as functions of space and time.
  • Gas and Compressed Air - Gas properties, capacities of pipelines, sizing of relief valves - air, LNG, LPG and more

Related Documents

Search the Engineering ToolBox

Engineering ToolBox - SketchUp Edition - Online 3D modeling!

3D Engineering ToolBox - draw and model technical applications

Engineering ToolBox - SketchUp Edition - add standard and customized parametric components - like flange beams, lumbers, piping and more - to your SketchUp model - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!