According to PV=nRT (ideal gas law), no you cannot in a closed system!!! But Hydrostor isn't violating any laws of physics -- they are simply capturing that heat so that it doesn't become waste heat!
Hydrostor has a thermal management system that captures the heat and stores is during compression. Then it reuses the heat when it is decompressing the air.[1]
This seem extremely promising as a much smaller footprint solution than pumped storage and much more sustainable and lower cost than any other energy storage solution. I just heard about them today, and I'm extremely impressed.
That doesn't seem isobaric. Searching if it's possible, I've seen mentions of condensing working fluids, and bumby mentions ocean floor bags which seem like a good solution.
An external pressure (usually water) keeps it at a constant pressure.
Think of a bag of air under water on the ocean floor. The height of the water column is (relatively) constant, so the pressure in the bag is also constant. The air is being compressed as it goes from sea level into the bag, but inside the bag, the pressure is always the same. If you define the system boundary as the bag, it's an isobaric system. The volume changes, but the pressure is constant. Contrast that to the compressor you might have in your garage where the rigid tank provides a constant volume, but the internal pressure changes.
