Summary: We consider a system of Markov processes of finitely-many particles which exchange their energies in pairs at random times. A law of large numbers for this system means that the empirical measures of the processes may be approximated (as the number of particles increases) by the solution of a nonlinear evolution equation (the so-called McKean-Vlasov limit). This work presents two results of this type. The first one concerns the empirical processes and gives a probabilistic method for solving the nonlinear equation. The second one is stated in the path scheme and extends classical results of chaos propagation by M. Kac [Proc. 3rd Berkeley Sympos. math. Statist. Probability 3, 171-197 (1956; Zbl 0072.428)] and H. P. McKean jun. [Lect. Differ. Equat. 2 (USA 1966-67), 177-194 (1969; Zbl 0181.444)].