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Fall of Caloric

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September 19, 2014

Sadi Carnot proposed that there is a limit on the fraction of heat energy that can be converted into mechanical work.  To re-use Carnot’s own illustration, the power of a waterfall is limited by how much water falls how far.  He reasoned that if the power is limited by how far the water falls, then there is a similar limit that he calls the fall of caloric.  “Caloric” is the colorful but imprecise terminology of the time that, in context, referred to either heat or entropy.  (Carnot may not have written the words heat and entropy, but he presented the subject very clearly.)

For any heat engine, including diesel engines, the maximum fraction of heat that can be converted into mechanical work is limited by the difference between the maximum and minimum (absolute) temperatures.  The fraction is simple:

Maximum Efficiency = 1 – (Minimum Temperature / Maximum Temperature)

To translate: maximum possible fuel economy increases as maximum temperature of the diesel in-cylinder gases increases.  In real life, this ideal can never be attained because of friction, but steady and continual advances in engine mechanisms have minimized friction.

The fraction embodies two other facts:  1) both hot and cold must exist for mechanical power to be possible and 2) conversion can never be 100% because the maximum temperature would have to be impossibly high or the minimum temperature would have to be absolute zero.

The genius of Rudolf Diesel was to apply Carnot’s principles to define how and when to add high heat to get very close to this maximum efficiency.  The Great Plains Diesel Technologies, L.C. continuously-controllable injector technology can make this happen.
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