  We present a (random) mechanical model consisting of two lottery-like
reservoirs at altitude $E_h$ and $E_l<E_h$, respectively, in the earth's
gravitational field. Both reservoirs consist of $N$ possible ball locations.
The upper reservoir contains initially $n_h\le N$ weight-1 balls and the lower
reservoir contains initially $n_l\le N$ weight-1 balls. Empty locations are
treated as weight-0 balls. These reservoirs are being shaken up so that all
possible ball configurations are equally likely to occur. A cycle consists of
exchanging a ball randomly picked from the higher reservoir and a ball randomly
picked from the lower reservoir. It is straightforward to show that the
efficiency, defined as the ratio of the average work produced to the average
energy lost by the higher reservoir is $\eta=1-E_l/E_h$. We then relate this
system to a heat engine. This thermal interpretation is applicable only when
the number of balls is large. We define the entropy as the logarithm of the
number of ball configurations in a reservoir, namely $S(n)=\ln[N!/n!(N-n)!]$,
with subscripts $h,l$ appended to $S$ and to $n$. When $n_l$ does not differ
much from $n_h$, the system efficiency quoted above is found to coincide with
the maximum efficiency $\eta=1-T_l/T_h$, where the $T$ are absolute
temperatures defined from the above expression of $S$. Fluctuations are
evaluated in Appendix A, and the history of the Carnot discovery (1824) is
recalled in Appendix B. Only elementary physical and mathematical concepts are
employed.
