Jacques Arnaud, Laurent Chusseau, Fabrice Philippe

American Journal of Physics, American Association of Physics Teachers, 2010, 78, pp.106-110

ABSTRACT

We discuss a model consisting of two reservoirs, each with N possible ball locations, at heights Eh and ElEh in a gravitational field. The two reservoirs contain nh and nl weight 1 balls. Empty locations are treated as weight 0 balls. The reservoirs are shaken so that all possible ball configurations are equally likely to occur. A cycle consists of exchanging a ball randomly chosen from the higher reservoir and a ball randomly chosen from the lower reservoir. We relate this system to a heat engine and show that the efficiency, which is defined as the ratio of the average work produced to the average energy lost by the higher reservoir, is 1−El/Eh. When nl is comparable to nh, the efficiency is found to coincide with the maximum efficiency 1−Tl/Th, where the temperatures Tl and Th are defined from a simple expression for the entropy. We also discuss the evaluation of fluctuations and the history of the Carnot discovery.

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