# Revisiting the Carnot Limit - Thermodynamics



## tanstaafl28 (Sep 10, 2012)

_*Breaking time-reversal symmetry in a thermoelectric device affects its efficiency in unexpected ways.
*_
Thermodynamic engines convert heat into useful work. Testing the optimal efficiency of these machines has been at the forefront of scientific developments ever since 1824, when Sadi Carnot showed that in a simple engine undergoing a reversible thermodynamic cycle, the ratio between used and wasted heat must be less than the ratio of the absolute temperatures of the cold and the hot reservoir. This Carnot limit is simply a statement of the second law of thermodynamics.

On a practical level, knowing the ideal efficiency of engines and other devices helps us compare the advantages of using and developing one technology versus another. This is particularly important today, as the world faces energy challenges that could be mitigated by using available resources more efficiently. At the same time, studying the efficiency of thermodynamic engines helps us understand fundamental ideas, such as the relationship between the work an engine performs and the information gained or lost in the process, or the implications of a system being microscopically versus macroscopically reversible in time.

In this spirit, Kay Brandner at the University of Stuttgart, Germany, and colleagues [1] report in _Physical Review Letters_ their calculated efficiency of a simple thermoelectric device that converts heat to electrical current (Fig. 1). They show that when the device operates in an external magnetic field—a condition that breaks time-reversal symmetry for the motion of electrons—the efficiency is significantly lower than previous studies predicted. The lower bound on efficiency occurs, they argue, because in addition to the requirement that entropy be greater than or equal to zero, charge must be conserved—a point that was missed in earlier work. Their findings improve our understanding of thermoelectric efficiency and may one day influence the design of thermoelectric devices for real-world applications.

The Carnot engine undergoes two isothermal and two adiabatic changes, and runs sufficiently slowly that the thermodynamic state of the engine at each step along the way is well defined. Carnot engines have an efficiency η C that depends on the temperatures of the two thermal reservoirs providing heat into and out of the engine. As typically framed, the Carnot cycle is considered macroscopically reversible, since it is infinitely slow and produces no entropy.









A simple three-terminal thermoelectric device that converts heat into electrical current. The circle is a simple conductor in thermal and electrical contact with two temperature and charge reservoirs (the hotter reservoir is in red, the cooler reservoir in blue.) The third terminal is a probe (yellow), which, on average, does not exchange any heat or particles with the conductor. Brandner _et al._ show that turning on the magnetic field B, can improve the efficiency of the device.


Physics - Revisiting Thermodynamic Efficiency


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