From the ideal gas law PV = nRT we get:
where P is pressure, V is volume, n is number of moles of a given substance, and T is temperature.
As pressure is defined as force per area of measurement, the gas equation can also be written as:
Area and volume are (length) and (length) respectively. Therefore:
Since force × length = work:
The physical significance of R is work per mole per degree. It may be expressed in any set of units representing work or energy (such as joules), units representing degrees of temperature on an absolute scale (such as kelvin or rankine), and any system of units designating a mole or a similar pure number that allows an equation of macroscopic mass and fundamental particle numbers in a system, such as an ideal gas (see Avogadro constant).
Instead of a mole the constant can be expressed by considering the normal cubic meter.
Otherwise, we can also say that:
Therefore, we can write R as:
And so, in terms of SI base units:
:R = .