The Ideal Gas Law
The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density.
In a perfect or ideal gas the correlations between pressure, volume, temperature and quantity of gas can be expressed by the Ideal Gas Law.
The Universal Gas Constant, R _{ u } is independent of the particular gas and is the same for all "perfect" gases, and is included in of The Ideal Gas Law:
p V = n R _{ u } T (1)
where
p = absolute pressure [N/m^{2}], [lb/ft^{2}]
V = volume [m^{3} ], [ft^{3} ]
n = is the number of moles of the gas present
R _{ u } = universal gas constant [J/mol K], [lb_{f} ft/(lb mol ^{ o } R)]= 8.3145 [J/mol K]= 0.08206 [L atm/mol K] = 62.37 [L torr /mol K]
T = absolute temperature [K], [ ^{ o } R]
For a given quantity of gas, both n and R _{ u } are constant, and Equation (1) can be modified to
p_{1} V_{1} / T_{1} = p_{2}V_{2}/ T_{2}(2)
expressing the relationship between different states for the given quantity of the gas.
Equation (1) can also be expressed as
p V = N k T (3)
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.
The Ideal Gas Law and the Individual Gas Constant  R
The Ideal Gas Law  or Perfect 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 (4)
where
p = absolute pressure [N/m^{2}], [lb/ft^{2}]
V = volume [m^{3} ], [ft^{3} ]
m = mass [kg], [ slugs ]
R = individual gas constant [J/kg K], [ft lb/slugs ^{ o } R]
T = absolute temperature [K], [ ^{ o } R]
This equation (3) can be modified to:
p = ρ R T (5)
where the density
ρ = m / V [kg/m^{3} ], [slugs/ft^{3} ] (6)
The Individual Gas Constant  R  depends on the particular gas and is related to the molecular weight of the gas.
See also Nonideal gas  Van der Waal's equation and constants , used to correct for nonideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles and how to calculate total pressure and partial pressures from Ideal gas law
Example: The Ideal Gas Law
A tank with volume of 1 ft^{3} is filled with air compressed to a gauge pressure of 50 psi. The temperature in tank is 70 ^{o}F .
The air density can be calculated with a transformation of the ideal gas law (5) to:
ρ = p / (R T) (7)
ρ = ((50 [lb/in^{2}]+ 14.7 [lb/in^{2}])*144 [in^{2}/ft^{2}]) / (1716 [ft.lb/slug. ^{ o } R]* (70+ 460)[°R])
= 0.0102 [slugs/ft^{3} ]
The weight of the air is the product of specific weight and the air volume. It can be calculated as:
w = ρ g V (8)
w = 0.0102 [slugs/ft^{3} ] * 32.2 [ft/s^{2}]*1 [ft^{3} ]
= 0.32844 [slugs ft/s^{2}]
= 0.32844 [lb]
Note!
The Ideal Gas Law is accurate only at relatively low pressures and high temperatures. To account for deviation from the ideal situation an other factor is included. It is called the Gas Compressibility Factor, or Zfactor. This correction factor is dependent on pressure and temperature for each gas considered.
The True Gas Law, or the NonIdeal Gas Law, becomes:
P V = Z n R T (7)
where
Z = Gas Compressibility Factor
n = number of moles of gas present
Compressibility factor  Z  for Air
For full table  rotate the screen!
Temperature [K]  Pressure [ bar absolute]  

1  5  10  20  40  60  80  100  150  200  250  300  400  500  
75  0.005  0.026  0.052  0.104  0.206  0.308  0.409  0.510  0.758  1.013  
80  0.025  0.050  0.100  0.198  0.296  0.393  0.489  0.726  0.959  1.193  1.414  
90  0.976  0.024  0.045  0.094  0.187  0.278  0.369  0.468  0.678  0.893  1.110  1.311  1.716  2.111 
100  0.980  0.887  0.045  0.090  0.178  0.264  0.350  0.434  0.639  0.838  1.040  1.223  1.594  1.954 
120  0.988  0.937  0.886  0.673  0.178  0.256  0.337  0.413  0.596  0.772  0.953  1.108  1.509  1.737 
140  0.993  0.961  0.921  0.830  0.586  0.331  0.374  0.434  0.591  0.770  0.911  1.039  1.320  1.590 
160  0.995  0.975  0.949  0.895  0.780  0.660  0.570  0.549  0.634  0.756  0.884  1.011  1.259  1.497 
180  0.997  0.983  0.966  0.931  0.863  0.798  0.743  0.708  0.718  0.799  0.900  1.007  1.223  1.436 
200  0.998  0.989  0.977  0.954  0.910  0.870  0.837  0.814  0.806  0.855  0.931  1.019  1.205  1.394 
250  0.999  0.996  0.991  0.982  0.967  0.955  0.946  0.941  0.945  0.971  1.015  1.070  1.199  1.339 
300  1.000  0.999  0.997  0.995  0.992  0.990  0.990  0.993  1.007  1.033  1.067  1.109  1.207  1.316 
350  1.000  1.000  1.000  1.001  1.004  1.008  1.012  1.018  1.038  1.064  1.095  1.130  1.212  1.302 
400  1.000  1.001  1.003  1.005  1.010  1.016  1.023  1.031  1.053  1.080  1.109  1.141  1.212  1.289 
450  1.000  1.002  1.003  1.006  1.013  1.021  1.029  1.037  1.061  1.091  1.118  1.146  1.209  1.278 
500  1.000  1.002  1.003  1.007  1.015  1.023  1.032  1.041  1.065  1.091  1.118  1.146  1.205  1.267 
600  1.000  1.002  1.004  1.008  1.016  1.025  1.034  1.043  1.068  1.092  1.117  1.143  1.195  1.248 
800  1.000  1.002  1.004  1.008  1.016  1.024  1.032  1.041  1.062  1.084  1.106  1.128  1.172  1.215 
1000  1.000  1.002  1.004  1.007  1.014  1.022  1.029  1.037  1.056  1.074  1.095  1.113  1.152  1.189 
Related Topics

Air Psychrometrics
Moist and humid air calculations. Psychrometric charts and Mollier diagrams. Aircondition systems temperatures, absolute and relative humidities and moisture content in air. 
Basics
Basic engineering data. SIsystem, unit converters, physical constants, drawing scales and more. 
Fluid Mechanics
The study of fluids  liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time. 
Gases and Compressed Air
Properties of air, LNG, LPG and other common gases. Pipeline capacities and sizing of relief valves.
Related Documents

Air  Molecular Weight and Composition
Dry air is a mixture of gases where the average molecular weight (or molar mass) can be calculated by adding the weight of each component. 
Air  SCFM versus ACFM and ICFM
Actual air compressor capacity (ACFM) vs. standard air capacity (SCFM) and inlet air capacity (ICFM). 
Charles' Law
Volume of an ideal gas vs. temperature. 
Compression and Expansion of Gases
Isothermal and isentropic gas compression and expansion processes. 
Critical Temperatures and Pressures for some Common Substances
Critical temperatures and pressures for some common substances like air, alcohol, ether, oxygen and more. 
Density vs. Specific Weight and Specific Gravity
An introduction to density, specific weight and specific gravity. 
Gas Mixtures  Properties
Gas mixtures and the ideal gas law, mass calculations, the individual gas constant and density. 
Gases  Dynamic Viscosities
Absolute (dynamic) viscosities of some common gases. 
Gases  Ratios of Specific Heat
Ratios of specific heat for gases with constant pressure and volume processes. 
Gases  Specific Heats and Individual Gas Constants
Specific heat at constant volume, specific heat at constant pressure, specific heat ratio and individual gas constant  R  common gases as argon, air, ether, nitrogen and many more. 
Helium  Thermophysical Properties
Chemical, Physical and Thermal Properties of Helium  He. 
Humid Air and the Ideal Gas Law
Pressure, temperature and volume in a perfect ideal gas like moist air (air with water vapor). 
Moist Air  Mole Fraction of Water Vapor
Mole fraction of water vapor is the ratio of water molecules to air and water molecules. 
Nitrogen  Enthalpy, Internal Energy and Entropy vs. Temperature
Enthalpy, internal energy and entropy of Nitrogen as an ideal gas. 
Nonideal gas  Van der Waal's Equation and Constants
The van der Waals constants for more than 200 gases used to correct for nonideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles. 
Rankine Efficiency
The efficiency of the Rankine cycle. 
Temperature
Introduction to temperature  including Celsius, Fahrenheit, Kelvin and Rankine definitions  and an online temperature converter. 
Total and Partial Pressure  Dalton's Law of Partial Pressures
How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law. 
Universal and Individual Gas Constants
The Universal and Individual Gas Constants in fluid mechanics and thermodynamics. Individual gas constants for the most common gases. 
Vapor and Steam
An introduction to vapor and steam. 
Zeroth Law of Temperature
The direction of heat flow.