Thermodynamics 101 question - ideal gas compression

[SherpaDoug]

I believe if I have an ideal gas in a frictionless piston & cylinder, and I use X energy to compress it to half its volume, it will get hot and the pressure will rise. If no heat is lost I will get X energy back when the gas pushes the piston back.
But if the compressed gas is stored until the added heat is lost and the gas reaches the initial temperature again, I will get less than X energy back when the gas pushes the piston back.
How do I tell how much energy is lost as heat and how much is stored as pressure and recovered?

I am trying to compare the merits of an air spring vs. a steel or fiberglass leaf spring to store energy over the course of several hours.

 

[jpanhalt]

Scroll to about half way down this article and read the section on "temperature." You will see there is not one simple answer. What is clear, if you allow the compressed air/gas to lose heat, you will lose a fair bit of energy.

John