David, This is a very interesting, complex and perplexing subject.
Your statement - "The fact that a heat source and sink is required for the engine to operate ..." - may not hold for all heat engines. It may be possible to extract energy from a single thermal reservoir if there is another reservoir of particles (most of) which possess a common conserved quantity, like spin, independent of its temperature. See - "Information erasure without an energy cost" http://arxiv.org/abs/1004.5330 There is a video of a presentation of this paper at the 'Workshop on Quantum Information and Foundations in Thermodynamics 2011' in the session 'Erasure of information under conservation laws' at URLs http://qutube.ethz.ch/item/4 - or - http://www.multimedia.ethz.ch/episode_play/?doi=10.3930/ETHZ/AV-00806356-e034-44f4-9580-e6404b8269c1 The complete set of videos for this workshop is at: http://qutube.ethz.ch/authors/ The problem also becomes quite subtle when the reservoir consists of entangled quantum particles, instead of classical particles. See - 'Heat-to-work conversion by exploiting full or partial correlations of quantum particles' http://arxiv.org/abs/1101.1325 Also extremely interesting is - http://arxiv.org/abs/1211.1772 - I am currently trying to read it. -- Lou Pagnucco David Roberson wrote: > Recently I have been exploring issues associated with thermodynamics since > it has been many years since I studied the subject. I wanted to > understand why certain rules apply and exactly what that suggests is > happening at the basic levels. This particular subject comes up often as > we analyze LENR devices and so it is useful to pursue. > > > I was considering the Carnot cycle and other heat engines when it became > apparent to me that this is nothing more than a statement that the COE > (conservation of energy) applies to these devices and that there is > nothing mysterious happening. The fact that a heat source and sink is > required for the engine to operate is easy to understand in the context of > COE. > > > The way I approached the topic was to consider an ideal gas that exists in > a given state. The average kinetic energy of the gas atoms is directly > proportional to the absolute temperature (K). If you double the > temperature then you double the kinetic energy of the particles. If you > halve the temperature, then you will find that the kinetic energy is > reduced to one half of the original value. > > > So, if I take a given volume of this ideal gas at any given temperature > and extract mechanical energy from it then only a portion of the original > energy remains. For this thought experiment I do not allow any other > paths for energy to escape. In a simple example lets extract 1/2 of the > kinetic energy from the experimental gas source. This would not be a bad > engine if it could convert one half of the available energy into > mechanical energy. The exhaust gas would thus have exactly 1/2 of the > original energy it had before it was put to work so its temperature must > be 1/2 the original value. > > > The Carnot efficiency is defined as 1-Tc/Th. In the example that I > reviewed the efficiency is 1-.5 or .5 which is 50%. This makes a great > deal of sense since my machine extracted exactly one half of the energy > that it could have taken if it operated on a perfect cycle exhausting 0 > degree gas. Someone with a different engine than mine would obtain better > results if the exhaust gas is ejected at lower temperatures and hence less > kinetic energy. It is important to notice that no energy is lost in this > operation. The remaining energy is resident in the form of kinetic energy > of the ideal gas molecules and might be extracted at some later time by > another process. > > > I hope that this post is useful to others and will help to burrow through > the complexity of thermodynamics in a way that makes the behavior > understandable to everyone. It will be interesting to consider the > emission of radiant energy using similar thought processes. Answers for > some of the difficult questions that have been recently discussed might > materialize as a consequence. > > > Dave >
