From the ideal gas law PV = nRT we get R = \frac{PV}{nT}, where
P is pressure,
V is volume,
n is the amount of a given substance, and
T is
temperature. As pressure is defined as force per area, the gas equation can also be written as R = \frac{ \dfrac{\text{force}}{\text{area}} \times \text{volume} } { \text{amount} \times \text{temperature} }. Area and volume are (length)2 and (length)3 respectively. Therefore: \begin{align} R &= \frac{ \dfrac{\text{force} }{ (\text{length})^2} \times (\text{length})^3 } { \text{amount} \times \text{temperature} } \\ \\ &= \frac{ \text{force} \times \text{length} } { \text{amount} \times \text{temperature} }. \end{align} Since force × length = work, R = \frac{ \text{work} }{ \text{amount} \times \text{temperature} }. The physical significance of
R is work per mole per kelvin. It may be expressed in any set of units representing work or energy (such as
joules), units representing 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 metre. Otherwise, we can also say that \text{force} = \frac{ \text{mass} \times \text{length} } { (\text{time})^2 }. Therefore, we can write
R as R = \frac{ \text{mass} \times \text{length}^2 } { \text{amount} \times \text{temperature} \times (\text{time})^2 }. And so, in terms of
SI base units,
R = . == Relationship with the Boltzmann constant ==