[zackmorris]

Gasoline has about 33 kWh/kg (118.8 MJ/kg):

https://en.wikipedia.org/wiki/Gasoline_gallon_equivalent

Unfortunately, internal combustion engines have a pathetic fuel economy since they run at low temperatures (around the boiling point of water). All heat engines are limited by the Carnot efficiency, which improves with higher temperature differential. In practice, other cycles like Otto, Diesel, Rankine and Brayton are lower than Carnot and improve with things like higher compression ratio:

  Carnot efficiency = (T.hot - T.cold)/T.hot
  where T is in Kelvin

https://en.wikipedia.org/wiki/Thermal_efficiency#Carnot_effi...

A low compression, naturally aspirated engine running at room temperature with nothing done to improve fuel economy runs at (373.15 - 298)/373.15 = 20% efficiency. I've heard figures as low as 8% for rubber meets the road efficiency in older passenger cars, which I believe, since we drove a ’68 Cadillac that got 5 mpg back in the 90s when gas was under $1 per gallon.

The best modern high compression engines typically achieve 25-30% efficiency at best. So I figure there are about 8-10 kWh/kg (28.8-36 MJ/kg) available in gasoline with modern vehicles. Cars built before ‘70s efficiency standards would be more like 2.5-3 kWh/kg (9-10.8 MJ/kg).

Unfortunately, it's not just that people don't care how ridiculously inefficient their vehicles are, it's that politicians corrupted by the fossil fuel industry and vehicle manufacturing lobbies never stop conspiring to lower efficiency standards:

https://www.vox.com/2019/4/6/18295544/epa-california-fuel-ec...

But I digress.

Electric motors typically run at about 95% efficiency, so we can probably assume 90% efficiency to the road. That’s over 10 times more efficient than classic cars!

Looks like Tesla lithium ion batteries are 0.254 kWh/kg (0.914 MJ/kg):

http://theconversation.com/teslas-batteries-have-reached-the...

Which is very close to the theoretical ideal for lithium ion of 0.294 kWh/kg (1.058 MJ/kg):

https://en.wikipedia.org/wiki/Energy_density#Tables_of_energ...

I'm having trouble finding energy densities for the new lithium sulfur batteries:

https://advances.sciencemag.org/content/6/1/eaay2757

https://advances.sciencemag.org/content/advances/6/1/eaay275...

I'm going to use their low number of 1200 mAh/kg, working between 1.7 and 2.5 V, so averaging 2.1 V (which is very inaccurate without integration), we can call it about 2.520 kWh/kg (9.072 MJ/kg). That would be about 10 times denser than Tesla batteries. Maybe they are estimating half the density in the real world due to packaging or something, in order to arrive at their "5 times longer battery life" headline.

So anyway, the real numbers are:

  Gasoline       33 kWh/kg    118.8 MJ/kg   (ideal)
  Gasoline       8-10 kWh/kg  28.8-36 MJ/kg (actual for modern vehicle)
  Gasoline       2.5-3 kWh/kg 9-10.8 MJ/kg  (actual for pre-70s vehicle
  Lithium sulfur 2.520 kWh/kg 9.072 MJ/kg   (ideal)
  Lithium sulfur 1.260 kWh/kg 4.536 MJ/kg   (actual)
  Lithium ion    0.294 kWh/kg 1.058 MJ/kg   (ideal)
  Lithium ion    0.254 kWh/kg 0.914 MJ/kg   (actual for Tesla)

My numbers might be off by a fair amount, but the important thing here is to think in orders of magnitude. Lithium sulfur is halfway to the energy density of classic cars and aircraft, with all the positives, like electric motors having 10 times the power as gas engines by weight, much higher torque, and substantially higher endurance/simplicity.

[credit_guy]

Gas engines with 40-45% efficiency are possible [1].

[1] https://phys.org/news/2019-06-efficiency-gas.html

[zackmorris]

Hey thanks for that! I didn't know that methane has low knock so could be thought of as a high-octane fuel (which allows for higher compression which translates to higher thermodynamic efficiency). That has promising ramifications for a future methane fuel economy, where hydrogen from high-temperature solar thermal electrolysis is combined with a carbon source (perhaps CO2 from the air) to create methane. Propane would be ideal due to its low pressure storage if its conversion from methane can be scaled up. But compressed natural gas (CNG) is fine as well with methane and the gasses have similar properties.

I was thinking about what I said about the Carnot cycle and maybe it wasn't quite accurate. I tend to think about the world through a first-order effects lens. So the easiest way to explain why a turbine is usually more efficient than an internal combustion engine is that the turbine runs at a much higher temperate.

But the gasses in an internal combustion engine can reach a fairly high temperature as long as it's beneath the sag temperature of the metal block (otherwise you get warped valves). There was a lot of nonsense in engines before fuel injection attempting to prevent preignition when the mixture passed by the valves (in order to run as lean as possible, which caused excess heat) that I always thought was pretty silly.

Also there was a lot of work in the 80s and 90s to make ceramic engines in order to run at a higher temperature that never went anywhere as far as I can tell. They would have been lubricated by graphite and basically last forever. I think they were abandoned due to brittleness, but they would be great today with a continuously variable transmission or as a generator running at constant RPM like with locomotives.

[credit_guy]

Ceramics never made it into internal combustion engines, but they did make it into jet engines. In particular the whole 737-MAX debacle is because of the fabulous new engine built by GE, which Boeing simply thought they cannnot not install it on their 737 (unfortunately, they did a patch work at that).

Here's a quote from [1].

"These “super ceramics” are as tough as metals, but they are also one-third as heavy and can operate at 2,400 degrees Fahrenheit—500 degrees higher than the most advanced alloys. This combination allows engineers to design lighter components for engines that don’t need as much cooling air, generate more power and burn less fuel."

2400F is about 1600K. If you plug this into the Carnot efficiency formula and use a T_cold of about 220, you get something like 86%. If they ever find a way to replace the silicon carbide they currently use with hafnium carbide, they can reach 90%

[1] https://www.ge.com/reports/space-age-cmcs-aviations-new-cup-...