Maximal work problem in finite-time thermodynamics

In this paper three problems are considered: (a) the maximal work that can be produced in a finite time in a thermodynamic system; (b) the minimal wor k which must be done in order to transform an equilibrium thermodynamic sys tem into a number of subsystems that are out of equilibrium with each other in finite time; and (c) the maximal power that can be achieved in a finite time. The mathematical features of these problems are investigated. It is shown that in many cases the limiting work processes here are processes whe re intensive variables are piecewise-constant functions of time, and that t hese functions take not more than some predefined number of values. It is d emonstrated that many results obtained for a number of particular systems ( heat engines, heat transfer) follow from the general conditions for limitin g processes derived in this paper. Conditions for limiting work regimes in mass transfer processes are obtained.