Abstract: Optimal configuration of heated gas expansion under the generalized radiative heat transfer law is researched. In the process to determine the Euler-Lagrange (E-L) curve, the single variable internal energy E(t) is used to determine the optimal configuration of gas expansion through eliminating the gas volume variable V(t) by using optimal control theory. The analytical solutions of gas E-L curve under square and cubic heat transfer laws are obtained. Optimal configurations of gas expansion under square and cubic heat transfer laws are compared respectively with those obtained by Taylor series expansion through numerical examples. The results show that the value of process time tm has great influence on the initial states E(0) and V(0), thereby directly influencing the optimal time variation relation of gas inner energy and volume in the E-L arc part. Finally, it can be found that the optimal configurations obtained by means of elimination are similar to those obtained by means of Taylor series expansion when the total time tm for the expansion is very short. Therefore, the approximate solution of E-L curve can be obtained by means of Taylor series expansion in case of .

Key words: Finite time thermodynamics, Generalized radiative heat transfer law, Generalized thermodynamic optimization, Maximum work, Optimal configuration, Optimal expansion