Exactly, this is why steam boiler engines became obsolete, because you can burn gas at a much higher temperature than boiling water.

Lower temp can only be viable if you reduce the work needed to run the engine, and can still output the needed work/energy.

This is related to why work and heat are both measured in joules.

No, this is not right. Most power generation is done by steam in the US (85%). Steam can get much hotter than boiling water, and it is cheap and makes no waste.

That doesn't have to do with temperature, it has to do with the efficiency of the engine.

Gas burns at a much higher energy than steam, so it's much easier to extract more energy with less fuel, making for a smaller form factor.

I should clarify I was talking about an engine here. Not a power generator.

What I said is correct though. You can compensate for lower temperatures with a more efficient engine & energy conversion, and of course more fuel/input.

Neither the “engine”/“power generator” distinction you are attempting to make, not the statement “gas burns at a higher energy than steam”, is physically meaningful. It is true that supercritical steam turbines operate at a lower temperature than gas turbines, and if the cold reservoir of the Carnot engines in question were at the same temperature, that would indeed make gas turbines potentially more efficient. But in fact gas turbine outlet temperatures are much higher. This is why adding a steam engine to the output of a gas turbine makes it more efficient. (This is called a “combined cycle power plant”.)

The actually relevant distinction is that gas turbines, like other internal combustion engines, have a much higher ramp rate than external-combustion engines like a steam turbine. This makes “peaker” gas turbines a crucial resource for establishing power grid stability.

Thanks for taking the time to write this informative post. I am grateful that HN is home to real engineers. :)

I am not a real engineer; I have never built a working heat engine, unless you count rebuilding a Volkswagen engine. But I'm glad my comment was helpful!