That 1-T
c/T
h that Adam wrote about is the Carnot efficiency. The reasons engine efficiencies don't exceed 40% in most typical applications are the ones we mentioned. Say the heat is dumped to a typical ambient environment at T
c=300K. To get Carnot efficiency above 40%, you need for T
h to be above 500K. That's perfectly possible, but you can't get a whole lot hotter than that without running out of suitable materials. If you then remember that the real efficiency is always less than the Carnot efficiency, both due to friction and the heat flow problem we mentioned above, it's rare to find examples much better than 40%.
I'm surprised, given the extraordinary sophistication of many of your questions, that you aren't familiar with the reason for the Carnot limit. As heat Q flows out of the hot reservoir, its entropy S goes down by Q/T
h. (That's by definition of T.) According to the second law of thermodynamics, no process decreases net S. So there must be a heat flow to the cold reservoir of at least (Q/T
h)T
c. That's energy not available to do work. So of the Q energy drawn from the hot source, what's left to do work is at most Q(1-T
c/T
h).
Mike W.
(published on 01/17/13)
