Key equations for Process Engineers Thermodynamics

Universal (R) Gas Constant

The universal or R gas constant is widely used in thermodynamics, let's look at the origin, definition and values (for different units) of this widely used number in thermodynamics.

The behavior of an Ideal gas is described by the following equation,

PV = nRT

where,

P = Pressure (bar, atmosphere, Pa)

V = Gaseous volume (m3, cm3)

n = number of gaseous moles (dimensionless)

R = Universal gas constant (J/mol.K, lit.atm/mol.K)

T = Temperature of the gas (K, 0C)

"R" is also known by alternative names such as Ideal gas constant, molar gas constant or simply, R gas constant.

The "R" gas constant is common for all the gases and the numerical value of this constant depends on the units used to describe the remaining entities in the Ideal gas equation, such as pressure, temperature, and volume.

R constant calculation

It is important to note that the universal gas constant or R is not an actual measurable physical entity. But it is rather a number that we have created to balance both sides of the ideal gas equation - PV = nRT.

Think of it this way - all the actual measurable physical properties of a gas already had different units of measurement. Gas properties like pressure, volume and temperature have been measured in different, independent units for a long time.

The quantity of gas contained in a mole is also characterized by the fixed Avogardo's number. Avogadro's law states that one mole of any gas contains the same number of molecules, equal to 6.02214 × 1023.

So to determine the value of R, we simply need to consider a thought experiment where we have taken 1 mole of an ideal gas (real gas with behavior closest to ideal). Put that gas at fixed volume (V) and temperature (T). Then measure it's pressure (P). Finally calculate the value of R as,

R = P×V ⁄ T

The value will change for different units. But universally it will remain the same for the ideal gas at any pressure, temperature or volume.

Universal Gas Constant Values

For different combinations of units, numerical values of R constant are given by following list,

Units ( P.V / n.T )                                          Value of R gas constant

J/K.mol                                                           8.314

cal/K.mol                                                        1.986

erg/K.mol                                                       8.314X107

lit.kPa/K.mol                                                  8.314

m3.Pa/K.mol                                                  8.314

cm3.MPa/K.mol                                             8.314

m3.bar/K.mol                                                 8.314X10-5

cm3.atm/K.mol                                               82.06

lit.bar/K.mol                                                   8.314X10-2

lit.atm/K.mol                                                  0.082

lit.mmHg/K.mol                                             62.364

lit.torr/K.mol                                                   62.364

ft.lbf/K.gmol                                                   6.132

ft.lbf/0R.lb-mol                                               1545.35

ft3.psi/0R.lb-mol                                             10.732

ft3.atm/0R.lb-mol                                           0.730

ft3.mmHg/K.lb-mol                                        998.97

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