This will probably take several posts.
Also you (I think) stated something about the bloom box not using the Carnot cycle. That makes their claims stranger still. The Carnot cycle is the most efficient process you can create without violating the second law of thermodynamics (and creating a perpetual motion machine). Other cycles can have the same efficiency, but not using the Carnot cycle is not an argument that implies the bloom box could be more efficient in not doing so.
Originally Posted by npita
I understand your confusion about Carnot's law. Lots of people throw it around without understanding it.
Someone else (".." is the userid) brought up Carnot's law, not me, but he is correct. Carnot's law does NOT apply to the Bloom box or any other fuel cell. Or to batteries, either. Fuel cells are electrochemical devices. The Carnot cycle only applies to heat engines.
I'll simplify this somewhat.
A heat engine is a device that takes energy in the form of heat from a reservoir at one temperature and puts heat energy out to another reservoir at a lower temperature, producing mechanical energy in the process.
A good example of a heat engine is a steam boiler and turbine in a coal fired power plant. The heat engine is the boiler through the turbine. The hot reservoir is the hot gas in the burner. The cold reservoir is the ambient air. The output of the heat engine is mechanical energy from the turbine that drives the generator.
Carnot's law says that the maximum energy efficiency of a heat engine is T1-T2/T1. T1 is the temperature of the hot reservoir, T2 is the temperature of the cold reservoir. Temperature is expressed in an absolute scale, such as Rankine, Kelvin or any other scale where Absolute zero = 0 degrees.
Carnot's law only applies to heat engines.
A fuel cell is not a heat engine. The heat energy in a fuel cell does no work, the heat produced by the device is simply a waste byproduct of the energy production. The fuel cell does need to be heated to a high temperature to function, but the heat produces no energy. In concept, a fuel cell would operate even if the ambient air was at the same temperature as the fuel cell itself.
The same concept would apply to a battery. An alkaline battery can operate with the internal parts of the battery being the same temperature as the surrounding air. If Carnot's law applied to batteries, a battery could not produce any energy at all. Carnot's law doesn't apply to everything, only to heat engines.
If a device is not a heat engine, Carnot's law does NOT limit the efficiency of the device. There may be other considerations that impose a limit on the theoretical efficiency of a fuel cell.
In theory, a fuel cell generation system could always exceed the efficiency of the Carnot limit. Simply take the fuel cell waste heat and use it to drive a Carnot cycle heat engine. You get the efficiency of the Carnot engine plus the efficiency of the fuel cell.
By the way, the Carnot cycle is not a characteristic of a fuel, it's a characteristic of a system. You can increase the Carnot limit of a system by increasing the temperature of the hot reservoir or decreasing the temperature of the cold reservoir. There are usually practical problems that limit the temperatures you can use, though.