Vo, This is simply an energy storage problem. Forget all the adiabatics, isothermals, reciprocating engines, Carnot, regenerators, multi-stage systems etc. etc.
In the ideal case you go up and down an adiabatic pretty damn reversibly - if you had a cylinder with a long piston. All that happens is at the compression station it goes up, then (on PV) goes down at constant volume, then goes down another adiabatic and comes out cold. The rejected heat goes to environment, some work is available in the car, and some of that work rejected to the environment comes back - herein lies all the icing up problems and inefficiencies in design. It's a kind of hysteresis. I suggested lagging the tank and coming up with means of keeping the pressure down and increasing the energy storage of the thing. All it's doing is acting like a SPRING, so why not use the real thing??? The gas is used as a storage medium where the energy is stored in random (non coherent) KINETIC ENERGY of the molecular motion hence all the thermodynamics getting in the way of a simple problem. Traditionally we've struggled with random motion and it leaking away. That's all the problem is, no mystery to thermodynamics or unassailable problems if you **get out the mind set**. Now, a SPRING stores the energy in a COHERENT manner as POTENTIAL ENERGY between the chemical bonds. If you keep it in the linear region (no deformation) then there is little hysteresis. It simply a question of what material you use. So we store work against a few MPa in a gas or work against a few GPa in a solid. Why not CLOCKWORK POWERED Tata cars??? I've never loved Thermodynamics and feel the subject gets locked up in lots of mysteries and "can't do rules of thumb" when it can be thought around or even have its premises totally re-thought. No bogey man subject here telling people what they can and I can't do. I've never like the subject because it gives me silly limits. Speaking artistically (and an engineer is 'artistic' (solves things from the human perspective, art is a human construct), he creates what has never been, where as a scientist discovers what is), it doesn't let you soar, constrains the imagination too much. So I don't like it as a subject. Relativity is like that too. Attack its premises and take it in new directions whilst constrained by experiment and logic as the honest research must be. Designs and thoughts without limits when you break out of Society's imposed rules. Break the mould it's no bogeyman "can't do this can't do" that subject. It strikes me a bit like music, ballet or architecture. They impose the rules then someone breaks the mould, then they say "what was the fuss?"
