One of the most critical aspects of the implementation of renewable electricity is the ability to store electricity.  If a good solution existed right now, our situation would be a good deal easier.  On the face of it, compressed air seems a likely candidate: relatively easy to make, store and use - so what is the problem?  Why isn't it used routinely?

More Thermodynamics than You Ever Wanted to Know?

We usually speak of storing and using energy without being very precise about what we mean.  That ends forever if you take a few chemistry or engineering courses.  Thermodynamics rules everything.