It’s closer to 19x when you consider engine efficiency. Heat is not that useful on it’s own.

Considering jets already do 9,500 mile flights a 500 mile range seems viable. But, if you start talking significant amounts of electric aircraft, very short landings for battery swapping are also possible. That's not going to get you to Hawaii, but it's still faster than taking a high speed train.

PS: You can also push these numbers as electricity is much cheaper than jet fuel. Electric engines also weigh less than batters which allows for a higher mass fraction for fuel. Shorter flights also have lower penalties for going slower. So, an optimized electric aircraft could probably make 800 miles with similar costs to current jets without any major breakthroughs.

Yes, and it could be viable for short flights with mountains between, where it's hard to build high speed rail, like flights LA<->Las Vegas.

Ops: Electric engines also weigh less than jet engines which allows for a higher mass fraction for batteries.

Really? I thought turbines were really excellent in terms of power to weight?

Currently you can get 10kw/kg turbines and 10kw/kg electric motors so they are close.

However, the turbines require more infrastructure around the turbine. Put another way, simply comparing fuel vs batteries ignores the weight of fuel tanks, fuel pumps, etc. We care about the system not just individual components. That said, the fact that burned fuel reduces aircraft weight is a huge advantage over batteries.