I'm not at all sure what you mean here by "lagging the cold sink".
Over here we sometimes call insulation lagging - sorry I didn't realise you guys didn't use the word that way, too. I should have looked that up, apologies. Anyhow, what I meant was insulating the cold sink. Oh, and 'cold sink' and 'heat sink' are interchangable in my book; a sink has to be comparatively cold in order for heat to be given up there.
In other words, if the fire extinguisher is discharged through such a turbo-generator the gas will be much colder than if it were simply discharged into the air without doing additional work.
Sorry if I gave the impression that I was arguing that an unheated expanding gas wouldn't cool, I've no doubt that you're right on that point. What I was trying to focus on was that it's possible to expand a gas at constant temperature, as long as you add heat energy to it at the same time. I was trying to argue that this was what happens in the idealised Stirling Cycle.
Sadly, there aren't many large supplies of hot, compressed gases just sitting around for the taking...
What about the earths atmosphere ?"
I was thinking of hotter, more compressed gases than that when I wrote my post. However, you've got a good point; there's nothing to stop you making an engine powered by differences in pressure or temperature in the Earth's atmosphere.
What we need in order to complete the Booth cycle is something that will absorb the heat energy from the gas. Unfortunately that has to be a sink that is colder than the gas. I believe it is impossible to have a heat engine in which the working gas falls to a temperature below that of the coldest sink in the engine.
I'm not so sure,
If we're talking about a thermodynamic cycle - where a working fluid is taken through a sequence of thermodynamic states, returning to it's original state, then I'm pretty sure that it will be necessary to reject some heat at some point. The reason I think this is because:
dS = dQ / T (from http://en.wikipedia.org/wiki/Entropy
ie the increase in entropy of a working fluid is equal to the heat transferred to the working fluid divided by the temperature at which that transfer occurs. Also, the decrease in entropy of a working fluid is equal to the heat transferred out of the working fluid divided by the temperature at which that transfer occurs.
So, if we add heat the working fluid at any point on the cycle then the entropy increases.
In order to get the working fluid back to to the state that it started from and complete the cycle, the entropy of the working fluid must be reduced back down to the value that it started at.
The only way for the entropy of the working fluid to reduce is for it to give up energy as heat. Losing energy by doing work alone does not reduce the entropy of the working fluid.
The only way for the working fluid to give up heat is for it to come into contact with something at a lower temperature than itself.
Note that if you want to reduce the entropy back to its starting value, then the amount of heat that you need to give up to do it will be lower the lower the temperature of the working fluid is when you give up the heat. That's why it's important for the cold sink to be cold.
Take the "free piston" type Stirling engine. For an example:
Here there is no flywheel to store energy to later compress the gas. It seems that the gas cools and contracts instantaneously on its own drawing the piston back to its starting position. How is this possible ?
Reading the discussion below the video you'll see that the builder and a commenter discuss a spring. The spring stores work and passes some back in compressing the working fluid in the same way that a flywheel does; the spring is a replacement for the flywheel.
A major thing to note is that at 2:08 he says that in his next iteration he's going to add fins to the sink: "The next stage is to... get some large cooling fins on the cold end to try and sink a lot more of the heat".
In effect, the light and heat being dissipated by the LEDs constitutes a kind of 'heat sink'
The LEDs are powered by the magnet moving in the coil. Any energy transferred to them from the working fluid will be in the form of work, rather than as heat. As I've noted above, I don't think that losing energy as work is the same as losing it as heat, as it doesn't reduce the entropy of the working fluid. Essentially, I don't think that the LEDs are equivalent to a heat sink.
Glass is a very poor heat conductor and yet this engine is running very rapidly. I don't believe that this can be explained by the idea that heat is being conducted away to the "heat sink" through the glass so rapidly or efficiently as would be required to keep this engine running at such a rapid pace.
I guess that may be one reason why he's planning to make the next one out of metal. I reckon it'll be running fast because it's not very heavily loaded. I certainly don't think anything is happening efficiently in this engine, great though it is. As I said in my previous post, I reckon you're right that a higher load will lead to better efficiency because it makes the engine run slower, giving more time for heat transfer.
I understand that you might not want to take my word for it; ask the guy who made it about the spring and whether he thinks insulating the sink would make it more efficient.
I hope my comments don't seem negative or critical, I certainly don't mean them to be. I find your posts very interesting and I'm enjoying spending time thinking them over. If you think I'm wrong on any point I'm arguing then that's fair enough - it won't be the first time I've been wrong, that's for sure. =]