Lessons · Engineering · Efficiency, and the ceiling nothing beats
The ceiling no engine beats
No heat engine working between two temperatures can be more efficient than one minus the ratio of the absolute temperatures, cold over hot. That is the Carnot limit. Real engines fall well below it, but nothing exceeds it, and the temperatures must be absolute.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
What it is for
It is the fastest sanity check in thermodynamics. Any claimed efficiency above the Carnot figure for its temperatures is wrong, and you can say so without knowing anything else about the machine.
How to think about it
Convert both temperatures to kelvin first -- this is the step that is skipped and it changes the answer completely. Then one minus cold over hot. Compare the claimed efficiency against that ceiling.
Worked example
Efficiency ceiling = 1 - (T cold / T hot).Absolute temperatures only.
Celsius to kelvin: add 273.Skip this and the answer is nonsense.
Real engines fall well below the ceiling.Friction, heat loss, irreversibility.
Nothing exceeds it.A claim above it is an error, not an invention.
Your turn
A cycle runs between 600 K and 300 K. Write the Carnot efficiency as a decimal.
1 - 300/600 =
Solve one, graded on the server
The trap
Using degrees Celsius. The ratio only means anything on an absolute scale, and Celsius gives an efficiency that can even come out negative.