Sean Breheny wrote: > If T0>T1, the heat flow is spontaneous, P1 is negative, and you can > actually get some useful work out of the system by using a heat > engine. > > If T0 "pump" the heat against the temperature gradient. However, the power > P1 which you input to the system also gets converted to heat and > contributes to Pf. So, you actually get Pf+P1 heat flow out into the > sink at temperature T1. Not really. You seem to be missing the whole concept of Carnot efficiency. One way to state Carnot efficiency is that it is the maximum theoretical efficiency by which work can be done from a temperature difference. This efficiency is quite simple to describe: Carnot efficiency =3D (Thot - Tcold) / Thot =3D Tdiff / Thot Thot =3D hot temperature, linear absolute scale Tcold =3D cold temperature, linear absolute scale Tdiff =3D Thot - Tcold =3D temperature difference This shows that the efficiency is low for small temperature differences relative to their absolute temperature. For example, suppose a heat engine was trying to extract work from 20C and 0C reservoirs. In absolute terms, the temperatures can be expressed as 293K and 273K. The Carnot efficiency is therefore (293K - 273K) / 293K =3D 6.8%. For every 100J of heat the hea= t engine lets flow from the hot to cold reservoirs, it can extract at best 6.8J of work. This is a inherent upper limit due to thermodynamics. It has nothing to do with inefficiencies in the heat engine itself. In fact, this assumes a theoretical maximally efficient heat engine. Real heat engines will of course produce less than the theoretical maximum of 6.8J of work per 100J o= f heat transferred. When specifying the "efficiency" of a heat engine, it should therefore be made clear whether this is the absolute efficiency or relative to the Carnot efficiency. Let's say a real heat engine produces 3J of work in the above example. You could say it is 3% efficient in that case, which is relevant if you just want to know how much you get out for how much heat you have to put in. However, you could also claim 3/6.8 =3D 44% efficiency. That may be more relevant if you're designing the heat engine and want to know how much room there is left for improvement. Back to the original point above. The same Carnot efficiency that says you can't get more than 6.8W of work when letting 100W flow from 20C to 0C also works in reverse. In other words, a perfect heat pump would only need 6.8W of input to make 100W of heat flow from 0C to 20C. Of course again real heat pumps will have some additional inefficiency. Let's say a real heat pump exists that requires 20W of input power to move the 100W of heat from 0C to 20C. That heat pump is only 6.8W/20W =3D 34% efficient, since a perfect heat pump would require less input power to do the same thing. However, you could also claim the pump is 100W/20W =3D 500= % efficient. In other words, for every Watt put in you get 500% of that out in heat. Neither efficiency claim is "wrong". Which one is relevant depends on circumstances. If you're trying to heat your house, then the 500% figure i= s actually useful. It tells you what you get for what you have to spend. In that case you don't care that it actually cooled the outside air a bit. Note that all the 20W put into the heat pump are not part of the 100W output. In this example, only 6.8W of it are. The other 13.2W heat up the motor, grind metal off gears, etc. Depending on how the heat pump is designed, it could add it's own waste heat to the output stream. In the example of heating your house, this could be the case if the heat pump was inside the house with only the cold connection to the outside. In that case, you get 113.2W of heat for 20W of electric power put in, or a "efficiency" of 566%. So the same heat pump in the same situation has a efficiency of 34%, 500%, or 566%, depending on what you care about and how you want to spin it. ******************************************************************** Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products (978) 742-9014. Gold level PIC consultants since 2000. --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .