The purpose of this paper is to define a finite-time closed Brayton cycle and apply it to an indirect gas-cooled nuclear reactor plant for its optimization. Practical engineering heat engine power optimization usually takes the form of determining minimum heat exchanger area per unit net power output or minimum cost per unit power output, rather than determining the maximum cycle efficiency. The objective function of the optimization described in this paper is specific power, power output per total heat exchanger surface area. The specific power output of a real indirect gas-cooled nuclear reactor plant coupled with its heat source and sink is analyzed. It is found that there is an upper bound on the specific power output of the nuclear power plant. This bound can guide the evaluation of existing real plants or influence design of future power plants.