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# 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/m2], [lb/ft2]

V = volume [m3 ], [ft3 ]

n = is the number of moles of the gas present

R u = universal gas constant [J/mol K], [lbf 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

p1 V1 / T1 = p2V2/ T2(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/m2], [lb/ft2]

V = volume [m3 ], [ft3 ]

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/m3 ], [slugs/ft3 ]                    (6)

The Individual Gas Constant - R - depends on the particular gas and is related to the molecular weight of the gas.
See also Non-ideal gas - Van der Waal's equation and constants , used to correct for non-ideal 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 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 (5) to:

ρ = p / (R T)                            (7)

ρ = ((50 [lb/in2]+ 14.7 [lb/in2])*144 [in2/ft2]) / (1716 [ft.lb/slug. o R]* (70+ 460)[°R])

= 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                               (8)

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 deviation from the ideal situation an other 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

### Compressibility factor - Z - for Air

For full table - rotate the screen!

Compressibility factor for Air - Z -
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

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Moist and humid air calculations. Psychrometric charts and Mollier diagrams. Air-condition systems temperatures, absolute and relative humidities and moisture content in air.
• ### Basics

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• ### Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
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Properties of air, LNG, LPG and other common gases. Pipeline capacities and sizing of relief valves.

## Related Documents

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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.
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• ### Compression and Expansion of Gases

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• ### 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.
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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.
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Chemical, Physical and Thermal Properties of Helium - He.
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Pressure, temperature and volume in a perfect ideal gas like moist air (air with water vapor).
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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.
• ### Non-ideal gas - Van der Waal's Equation and Constants

The van der Waals constants for more than 200 gases used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles.
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Introduction to temperature - including Celsius, Fahrenheit, Kelvin and Rankine definitions - and an online temperature converter.
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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.
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An introduction to vapor and steam.
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The direction of heat flow.

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## Citation

• The Engineering ToolBox (2003). The Ideal Gas Law. [online] Available at: https://www.engineeringtoolbox.com/ideal-gas-law-d_157.html [Accessed Day Month Year].

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8.21.8

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