Yes, absolutely, provided you could insulate it so the stored hot gas doesn’t lose any heat, then you could recover all of the work that went into compressing it.
The equation for work done by a mass of idea-gas working fluid during an adiabatic compression or expansion is:
W =(p2V2−p1V1)/(1/gamma)
If you start at state P1,V1 and compress to state P2,V2, the fluid does W amount of work (W<0). If you then flip it around - swap the state 1 and state 2 values - you get W amount of work out of the fluid (W>0). The exact same amount.
No crabbiness here, just a claim that you are incorrect. If you disagree, then I invite you to explain why the above equation is inapplicable to either the compression process, the expansion process, or both.
Machine Elf - As far as I know the 2nd law of thermodynamics is an empirical law that has been accepted historically. I personally can’t prove it to you. Maybe you can ask the other physicists on the board.
What you are stuck on is called a “reversible process” used to teach introductory thermodynamics. In reversible processes heat and work are interchangeable. But that is an imaginary world - in the real world, at the macroscopic level - this never happens. Carnot engine efficiency is pretty much the limit for converting heat into work.
In the real world, thermal losses and mechanical friction will prevent perfect 100% work recovery from a compression/expansion sequence, but this are not the things that the Carnot efficiency limit refers to.
It would indeed be useful if one or more other engineers on the board would chime in here.
Assuming it was possible to fly across the country on one charge (and assuming the battery weight and size was the same as a full jet fuel load), what is the theoretical maximum speed of all-electric “jet” engines on say, a typical airliner?
Xema stated upthread that jet fuel has a 20:1 energy density advantage over the best batteries. So with only 5% of the energy at your disposal for your transcontinental flight, you’d need to fly the plane in a way that only generates 5% of the drag. Aero drag scales as the square of speed, so 1/20 of the drag means 22.4% of the speed. Modern airliners cruise at about 550 MPH, so if you’re going to cover the distance, your electroplane needs to cruise at 123 MPH. Which, frankly, isn’t enough to keep it in the air.
This assumes you’re using your battery energy to power high-bypass turbofan engines in the same way that jet fuel does (i.e. with an electrically-powered gas turbine engine at the center), and therefore generating thrust with comparable efficiency. If you’re using your battery energy to power electric motors that run ducted fans, you’d expect considerably better efficiency, so you’d be able to go faster - maybe even fast enough to stay in the air for the entire flight.
The problem is that that this is one hell of an assumption.
It’s like saying “assuming my toddler can pedal fast enough, can he beat a topfuel dragster on the 1/4 mile”? Well, yes. but the assumption is nonsense.
So is your assumption above. Battery energy density is WAY below hydrocarbon fuel energy density.
It’s not like saying that. In your toddler-versus-dragster scenario, your starting assumption is baked into the answer (“assuming my toddler can pedal fast enough to beat a dragster, can he beat a dragster?”); it’s a tautology. Ashtura stated the constraints of the problem (non-stop transcontinental flight starting with 40,000 pounds of batteries on board instead of 40,000 pounds of fuel), and asked what was possible in terms of top speed.
I admit that the result stemming from those assumptions - a ~16-hour flight from New York to LA - is not likely to be commercially viable unless jet fuel becomes extremely expensive.
A gas turbine is a gas turbine, apparently. The GE CF6 series of aviation gas turbines, used in the Boeing 747/767, Airbus A300/310/330, Lockheed C5 Galaxy, McDonnell Douglas DC-10/MD-11.
Its marine/industrial derivatives the LM2500/5000/6000 are used in multiple warship classes, including the US Navy’s Spruance, Kidd, and Burke class destroyers, the Perry class frigates, Ticonderoga class cruisers, and multiple other ship classes in other navies, including the Franco/Italian FREMM class frigates (which the US Navy is going to build under license). And they’re also used as stationary powerplants as you mentioned- peaking plants and backup generators.
Pretty much. The only difference is what you do with the hot, high-pressure gas after your compressor and combuster have created it (and after a turbine has taxed some energy out of it to keep the compressor section running):
You can fire it out the back end as a high-speed stream of gas to produce thrust, as on a fighter jet.
Or you can pass it through a second turbine to harvest mechanical shaft power. This is what turbine-powered helicopters do, as well as turboprop aircraft. It’s also how you use a ground-based gas turbine engine for power generation. The resulting exhaust stream does not produce significant amounts of thrust.
Or you can do some combination of the two. This is what a high-bypass turbofan engine is: some thrust is developed by the central gas turbine, and some thrust is developed by the large fan disk that’s driven by shaft power harvested from the exhaust stream.
As a reminder, the legal requirement for IFR flight is that you need to have the range to fly to your destination airport, plus be able to divert to a designated alternate, plus 30 minutes. For VFR flight, you need fuel to fly to your destination, plus 45 minutes of additional flight time.
I don’t know of a single electric airplane that can meet these requirements with any sort of reasonable range, outside of extreme range attempts in very lightweight specialized planes… Some of them don’t even have enough duration to meet reserve requirements at zero range.
There is an electric drivetrain called the Magni-X which can replace an engine or turbine in the 500-750 hp range (i.e. a PW PT-6 turboprop). A Beaver aircraft with the Magni-X powerplant is flying. It has a duration of 30 minutes with 30 minute reserve. The company certifying the plane uses them for water taxi, where the duration of the flight is typically 15-20 minutes. By swapping batteries with fresh ones at each end of the leg, they might make this work. To date this is the only feasible commercial use of electric flight I have seen that might be certified within a couple of years.
There is no way a current jet airliner could be converted to electric flight. Perhaps light turboprops like King Airs or maybe a Dash-7 could be used, if you are willing to lose maybe 80-90% of your range. But I could imagine an electric commuter service using such airplanes between two cities less than 100 miles apart. Sling a battery pod below the craft like the cargo pod in a Cessna Caravan, and swap them at each end of the leg like the electric Beaver. That’s at least in the realm of near-term feasibility with only small improvements in batteries and packaging.
