The physical basis and application of the fundamental relationship governing the balance and utilization of available energy for a chemical rocket operating within the atmosphere is described in detail. This vehicle-based exergy relationship is based on the global control volume analysis of an aerospace vehicle in flight. It provides the analytical balance between vehicle force power, the available energy of the propellant carried by the vehicle, and losses (due to irreversibility as quantified by the generation of entropy) inside and over the vehicle, and in the vehicle wake. The relative contributions of the thermochemical availability and the kinetic energy of the stored propellant to the overall energy availability are described; the kinetic energy of the stored propellant becomes a significant portion of the overall availability at high flight velocities. Analysis of the balance relationship shows that there are theoretical optimal flight velocities at a given altitude for which 1) overall entropy generation is minimized and 2) effectiveness of the conversion of available energy to vehicle force power is maximized. Methodology necessary to comprehensively utilize the balance relationship for a specific vehicle in flight is provided in detail, in terms of modeling of external aerodynamics, propulsion system, and the wake process. Specific propulsion and wake models for both hydrogen-oxygen and hydrocarbon-oxygen rocket engine operation are formulated with second-law accounting. These models are then used to develop parametric maps of rocket performance, defined in terms of energy availability of propellant, entropy generation, and conventional performance metrics for wide operational ranges of altitude, flight velocity, and oxidizer-to-fuel mixture ratio. Results verify theoretical observations regarding flight conditions that are required for minimum entropy generation and maximum utilization of energy availability. These propulsion models and available flight data are then utilized to provide the evolution of important second-law characteristics for the flight of the Apollo 11 (Saturn V) legacy system from launch to second stage burnout.