Heat engine with with state change and no cooling

[goran d]

I will look at two different engines, which need heater, and no cooler, to operate.
First one:
A rocket engine, which, instead of burning fuel, simply heats up cold fuel in solid form so the heated and evaporated substance is used as a reaction mass. The nozzle of the rocket engine is in vacuum, so there is no limit on the exit pressure. The gas expands so much, that the vast majority of it is cooled so much that it turns back into solid. This engine starts with cold solid fuel, adds heat, does work, and then ends up again with solid cold exhaust, which can be reused. The only drawback is that there are losses as, I think, it isn't possible to convert 100% of the exhaust to solid.

The second one:
This engine doesn't have the fuel loss problem.
The engine has a cylinder and a piston that can move inside of it. For the purpose of this description we assume the volume between the piston and cylinder is minimal when the piston is in top position. In between the cylinder and the piston there is a substance that's gaseous under environment temperature, for example carbon dioxide. There is a heat exchanger in the top part of the cylinder, which can heat up to environment temperature. At the bottom side of the cylinder there is an attached vacuum camera so that the piston doesn't receive air pressure.

The engine works as follows:

Initial state: The piston is in top position. The substance is cold, mostly in solid phase, with minimal amount of gas.
Stage 1: The piston is held in top position. The heat exchanger heats up the substance until it all evaporates and reaches environment temperature, greatly increasing pressure.
Stage 2: The piston moves down. The substance expands, and pushes the piston, doing work in the process. The expansion continues until the substance is so cold that it solidifies, leaving only negligible amount of gas. Note that due to no air pressure on the piston, the expansion does useful work during the whole stage 2, since it doesn't need to overcome air pressure.
Stage 3: The piston moves up, doing work on the remaining gas, compressing it. It continues until it reaches top position. Note that the useful work in stage 2 is much greater than the work in stage 3, since in stage 3 only a negligible amount of gas is compressed.
At the end of Stage 3, the engine is back in the initial position.

 

[256bits]

Did you do, or rather you should do a thermodynamic analysis to back up your claims.

This engine starts with cold solid fuel, adds heat, does work, and then ends up again with solid cold exhaust, which can be reused

One problem is the collection of the "solid cold exhaust" for reuse.

 

[goran d]

"Did you do, or rather you should do a thermodynamic analysis to back up your claims."

Unfortunately I don't know how to model state change.

 

[Drakkith]

The gas expands so much, that the vast majority of it is cooled so much that it turns back into solid. This engine starts with cold solid fuel, adds heat, does work, and then ends up again with solid cold exhaust, which can be reused.

The gas MUST leave the vehicle in order to generate thrust.

Stage 2: The piston moves down. The substance expands, and pushes the piston, doing work in the process. The expansion continues until the substance is so cold that it solidifies, leaving only negligible amount of gas. Note that due to no air pressure on the piston, the expansion does useful work during the whole stage 2, since it doesn't need to overcome air pressure.
Stage 3: The piston moves up, doing work on the remaining gas, compressing it. It continues until it reaches top position. Note that the useful work in stage 2 is much greater than the work in stage 3, since in stage 3 only a negligible amount of gas is compressed.
At the end of Stage 3, the engine is back in the initial position.

This seems plausible to me, as you would need a continuous supply of energy to heat the "fuel" up, so it doesn't seem to violate any laws of physics to me.