And ... you can move heat through walls.

Pressure is Heat times Density, and pressure can't go through walls.

Its easy to overlook that heat can go through walls, allowing many ways to return Engine Volumes to their initial condition, without doing significant work.

Not only can you move heat through walls, temperatures of similar masses of Vapor can actually be switched in place, all without performing more than tiny amounts of work.

If the pressure of the Vapor's is not "pushed" against or its volume changed, this operation is independent of pressure. A few ounces of force will easily move the mass of vapor around.

When an engine volume produces work by expanding to its practical limit, depending on the engine design or Pressure Envelope, the volume contains some unconverted heat, and is larger than its initial state. Paraphrasing the 2nd Law of T, now you are stuck, ( unless something else changes.) So, change something else. Move the heat to a constrained volume prior to expansion.

This is an essential step in making a Heat Recycling Engine. (One that works).

(Patents are pending for total heat recovery for real recycling engine designs.)

Counter Flow heat Exchangers

Are well known, but well ignored. Usually they are a couple pages from where your physics book says Diffusion is irreversible.

Here is one way to achieve reversibility of diffusion, to use counter flow to actually switch, not average out, the temperatures of two fluids. If the fluids are the same type and mass, the only limit on how close this can be to 100% switch is materials and construction. Over 90% is easily achievable.