Camot efficiency

Thermal Brownian motors can function as a motor, a heat pump, and a refrigerator. But can they reach Camot efficiency As we explained in some detail above, arguments have been raised against this possibihty [11-17]. On the other hand, a number of alternative constructions have been proposed for which it is claimed that Camot efficiency can be reached [24—29]. 

The industrial economy depends heavily on electrochemical processes. Electrochemical systems have inherent advantages such as ambient temperature operation, easily controlled reaction rates, and minimal environmental impact (qv). Electrosynthesis is used in a number of commercial processes. Batteries and fuel cells, used for the interconversion and storage of energy, are not limited by the Camot efficiency of thermal devices. Corrosion, another electrochemical process, is estimated to cost hundreds of millions of dollars annually in the United States alone (see CORROSION AND corrosion control). Electrochemical systems can be described using the fundamental principles of thermodynamics, kinetics, and transport phenomena. 

While the Seebeck effect enables TE devices to be used for power generation, the Peltier effect allows them to be used for cooling. In Peltier effect devices, heat flows in the same direction as majority carriers. The appropriate metric for this apphcation is called the TE efficiency, t], which is simply the ratio between the load s power input and the net heat flowrate. Essentially, rj gives the fraction of Camot efficiency attainable... 

It can be shown that the Camot efficiency may also be expressed as... 

For comparison, Camot efficiency (700°C and 60.1°C) which are the temperature levels of working fluid (steam) in the closed-loop power cycle... 

Because batteries direcdy convert chemical eneigy to electrical energy in an isothermal process, they are not limited by the Camot efficiency. The thermodynamic efficiency 8 for electrochemical processes is given by ... 

Nicolas Leonard Sadi Carnot, the French engineer and physicist, was bom in Paris in 1796. His father, Lazare Nicolas Marguerite Carnot, was in the French military service. Sadi Camot is considered as the founder of modem thermodynamics. Famous for his invaluable contributions to science and thermodynamics, Sadi Camot was honored with the title Father of Thermodynamics. Some of his noteworthy contributions to thermodynamics are the concepts of Camot heat engine, Camot cycle, Carnot s theorem, Camot efficiency, and reversible cycle. 

The Camot efficiency is the theoretical maximum efficiency by which a heat engine can do work when operating between two temperatures. The greater the difference in temperatures, the greater is the efficiency by which heat can be converted into work. 

The significance of the reversibility of the above processes is that at the end of the cycle the system is brought back to its starting point with no losses incurred due to friction or other causes. Thus, as the system temperature is restored to its starting point T, its pressure is also restored to its starting level of P. If the processes are not reversible, additional work woirld have to be done on the system to bring the pressure back to P,. The net work would be less than G2 Gn and the efficiency would be lower than the Camot efficiency. 

Show that ° for a Carnot cycle, derive the Camot efficiency formula. 

---