I have not done any physics in ages and have recently started studying it. The first chapter in my book deals with the ideal gas constant:
$$pV=nRT$$
It is rewritten as:
$$R=\frac{pV}{nT}$$
When I write it in SI units, it looks like this:
$$8.31\frac{\rm J}{\rm mol\,K} = \frac{(\rm Pa)(m^3)}{\rm (mol)(K)}$$
How does $\rm (Pa)(m^3)$ translate into joules?
The joule is the amount of energy needed to apply one newton of force for a distance of one meter: $$ \rm J=N\cdot m=\frac{kg\,m^2}{s^2}\tag{1} $$ Where the 2nd equality comes from the definition of the newton (mass times acceleration): $\rm N=kg\,m/s^2$. The pascal is defined as one newton of force applied to a one-square-meter area: $$ \rm Pa=\frac{N}{m^2}=\frac{kg}{m\,s^2}\tag{2} $$ Comparing (1) and (2) (specifically the last two equalities), we see that $$ \rm Pa\cdot m^3=\frac{kg}{m\,s^2}\cdot m^3=\frac{kg\,m^2}{s^2}\equiv J $$
If a constant pressure of $1\,\rm Pa$ is exerted on a piston, and pushes it back so as to liberate a volume of $1\,\rm m^3$, then the work done by pressure on the piston amounts to $1\,\rm J$.
