Reply to a non-scientist who asked, at a public discussion on energy, why the thermodynamic efficiency of a standard power plant is so low (35-45%)

Hi, Pat,
    35% is low, for the very oldest coal-fired or nuclear plants; new coal-fired plants hit 45%.  There are fundamental thermodynamic limitations to efficiency of a heat engine.  The limit discovered by Sadi Carnot about 150 years ago is firm: the maximum efficiency for a heat engine operating between a high temperature T2 and a low temperature T1 is (T2-T1)/T2.   All temperatures are absolute (Kelvin, or, if you're stuck in US units, Reaumur).  A few points:

• The practical high temperature is that of the working fluid (steam, up to about 600oC or 873 K), not that of the combustion stream (max. is about 2000oC or 2273 K; maximum practical T is 1200oC or 1473 K)).  
• The practical low T = T1 is just above the boiling point of water at normal atmospheric pressure - maybe 110oC = 383 K.  This is a bit higher than ambient temperature, which averages about 20oC = 293K nationally.
• So, having to work with a practical fluid (water) cuts our maximum efficiency from (1473-293)/1473 = 0.80 = 80% to (873-383)/873 = 56%
• Add in losses in generators plus energy use to run coal conveyors, sulfur-dioxide scrubbers, etc., and we're down to 45%.
• Nuclear plants have had to operate at lower temperatures, cutting their efficiencies.  Newer designs work at higher T and higher efficiencies.
• Fuel cells can do better, maybe 80%, not being heat engines.  They work best with very simple fuels such as hydrogen or methanol. 
• We can convert coal to syngas (hydrogen and carbon monoxide) or further to methanol.  There is a necessary loss of efficiency here (any process occuring at a finite rate operates at < 100% efficiency, according to thermodynamics)
• They're easily poisoned by sulfur --> S removal costs $$ and costs some energy.
• They also carbonize and stop working if the fuel contains carbon
• They have low power densities.  To make any power plant would need an enormous investment in $$ and materials.  Those materials cost a lot of energy to make, so it would be a loss, energetically, to use even the most advanced fuel cells for practical power plants.
• Fuel cells hold more promise for small-scale use - in fact, they're used in some hospitals and other medium-sized institutions.  They're being developed for cars but are still far from practical.  Of course, once we start distributing fuel, there are costs in $$ and energy to do this (pumping costs, trucking costs...)

So, in short, higher efficiencies in central power generation, or even medium-scale power generation, are a ways off in time.  Many, many people are working to advance this, but the technology is not there yet.  We can't stop pushing hard for this.

Cheers,
   Vince