These notes concern the material covered by the authors during 4 classes on the Escola Brasileira de Mecânica Estatística, University of São Paulo at São Carlos, February 2004. They are divided in almost independent sections, each one with a small introduction to the subject and emphasis on the computational strategy adopted.

A idéia central desse artigo é chamar a atenção para o uso do diagrama T x s na descrição das máquinas térmicas reversíveis. Este diagrama mostra-se extremamente adequado e eficaz no ensino da segunda lei da tertermodinâmica dos processos reversíveis, no entanto uma escolha mostra-se mais apropriada que a outra quando se pretende salientar a universalidade dessa lei e não restringir a análise a uma substância de operação específica com é gás ideal.

The central idea of this article is to call attention for the use of the T x S diagram in the description of reversible heat engines. This diagram is an extremely suitable and efficient way for teaching the second law of thermodynamics, following the Kelvin formulation. The conjugated pairs (PV) or (TS) are equivalent in the description of the reversible thermodynamic processes, however one choice is more appropriate than the other when one intends to point out the universality of this law and not to restrict the analysis to a specific operating substance like the ideal gas.

A 1 = L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18; 22;... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at p c for an annulus with aspect ratio r = 1=2 is estimated as C = 0.876657(45).