Optimal expansion of a heated ideal gas with time-dependent heat conductance

The optimal configuration of the expansion process of a heated ideal gas inside a cylinder for maximum work output with a movable piston and time-dependent heat conductance is determined in this paper. The heat conductance of cylinder walls is not a constant, but depends on the time-dependent heat transfer surface area of the walls in contact with gas. Euler-Lagrange formalism is applied to obtain the optimal process that maximizes the work output of the working fluid with fixed initial energy, initial volume, final volume and total time allowed for the expansion. The method of exhaustion is applied to determine the optimal initial value of internal energy of the Euler-Lagrange arc. Numerical examples for the optimal configurations with time-dependent heat conductance are provided, and the obtained results are compared with those obtained with constant heat conductance. The results show that the optimal initial value of internal energy of the Euler-Lagrange arc, the time corresponding to the maximum optimal internal energy and the time spent on the compression process with time-dependent heat conductance are quite different from those obtained with constant heat conductance. In addition, the volume and internal energy along Euler-Lagrange arc obtained with time-dependent heat conductance are much sharper compared with those obtained with constant heat conductance. Copyright , Oxford University Press.