For anyone curious, Carnot efficiency is the maximum efficiency of extracting work from a temperature differential:
Carnot efficiency = 1 - Tc/Th = (Th - Tc)/Th <- I find the last form easier to remember
Where temperatures are in Kelvin. So in this case 500 C and -160 C are 773 K and 113 K so:
Carnot efficiency = (773 - 113)/773 = 85.4%
It’s a handy approximation for the most efficiency that could be expected from other cycles. So for example an internal combustion (Otto cycle) engine running below the temperature of boiling water would have an expected efficiency at room temperature of about 68 F or 20 C or 293 K of:
Carnot efficiency = (373 - 293)/373 = 21.5%
Whereas jet (Brayton cycle) engines may have a temperature differential of 1000 C:
Carnot efficiency = (1293 - 293)/1293 = 77.3%
Things are a bit more complicated than this because with active cooling it’s not just the temperature of the engine’s components, but the temperature of the exhaust gasses, efficiencies of valves, compressors, turbines, etc. So modern internal combustion engines may reach 25% efficiency and turbines may reach 45% efficiency but I still find the Carnot cycle good for guestimation.
So for example, I remember research in the 90s for making ceramic internal combustion engines lubricated with graphite or exhaust that would run at a higher temperature and have an efficiency closer to jet engines. There were also working Stirling engine cars that would have gotten significantly better mileage because it’s more practical to approach the Carnot limit with the Stirling cycle than the Otto cycle:
The main tradeoff is that there hasn’t been as much research in high compression Stirling engines so they tend to have a higher volume than internal combustion engines at the same power output. But since Stirling engines have significantly fewer moving parts and use external combustion (meaning they can run on any fuel), I could never quite figure out why they were never mass produced. Perhaps if they had been, we would have seen industrial sized Stirling engines with Argon as the working fluid decades ago.
Then again, before the web and Wikipedia it would have been hard to make these kinds of points at a Thanksgiving dinner table.
Carnot efficiency = 1 - Tc/Th = (Th - Tc)/Th <- I find the last form easier to remember
Where temperatures are in Kelvin. So in this case 500 C and -160 C are 773 K and 113 K so:
Carnot efficiency = (773 - 113)/773 = 85.4%
It’s a handy approximation for the most efficiency that could be expected from other cycles. So for example an internal combustion (Otto cycle) engine running below the temperature of boiling water would have an expected efficiency at room temperature of about 68 F or 20 C or 293 K of:
Carnot efficiency = (373 - 293)/373 = 21.5%
Whereas jet (Brayton cycle) engines may have a temperature differential of 1000 C:
Carnot efficiency = (1293 - 293)/1293 = 77.3%
Things are a bit more complicated than this because with active cooling it’s not just the temperature of the engine’s components, but the temperature of the exhaust gasses, efficiencies of valves, compressors, turbines, etc. So modern internal combustion engines may reach 25% efficiency and turbines may reach 45% efficiency but I still find the Carnot cycle good for guestimation.
So for example, I remember research in the 90s for making ceramic internal combustion engines lubricated with graphite or exhaust that would run at a higher temperature and have an efficiency closer to jet engines. There were also working Stirling engine cars that would have gotten significantly better mileage because it’s more practical to approach the Carnot limit with the Stirling cycle than the Otto cycle:
https://www.youtube.com/watch?v=H_Vnxapd5fs
The main tradeoff is that there hasn’t been as much research in high compression Stirling engines so they tend to have a higher volume than internal combustion engines at the same power output. But since Stirling engines have significantly fewer moving parts and use external combustion (meaning they can run on any fuel), I could never quite figure out why they were never mass produced. Perhaps if they had been, we would have seen industrial sized Stirling engines with Argon as the working fluid decades ago.
Then again, before the web and Wikipedia it would have been hard to make these kinds of points at a Thanksgiving dinner table.