Another Engine

This diagram is the cycle for another heat engine (using a black hole as the working substance) that I studied in the recent paper. It is a path made of two constant pressure legs (isobars) and two constant volume legs (isochores) that happen (due to the properties of static black holes) to also be adiabats. See the post.

It got included in the paper as another example where one could compactly write down something useful about the efficiency, since, as it turns out, you can write closed form expressions for two quantities called the specific heat at constant volume and the specific heat at constant pressure. Then you can, in a limit get an expression for the efficiency. In the limit where the pressures are large, you can get a lot of work out for little heat, and so again the extreme case should give you the Carnot efficiency, and indeed that’s what you can see with a little algebra, as I put into the paper.

On the lighter side, I was, in a working draft, calling this the “World Engine”, for no other reason than to give me the excuse to have the caption “Release the World Engine!” in the figure showing the cycle. It’s just a silly joke based on a line the excellent actor Michael Shannon has in last year’s not-as-disasterous-as-I-thought-it-might-be Man of Steel movie.

-cvj