The problem of optimizing the thermal processes in a variable air volume (VAV) of heating, ventilating and air conditioning (HVAC) system is explored. Steady-state models of HVAC system components are developed. These models are interconnected to simulate the responses of the VAV system. The constrained optimal control problem is formulated and solved for two cases: one with constraints on zone-humidity ratio and one without. Typical daily optimal operating trajectories for the system are presented. Results show that to achieve thermal comfort, both zone temperature and humidity ratio should be controlled. The use of outdoor-air-for-free-cooling is also studied as an optimization problem and the resulting optimal outdoor air-flow rates and energy savings are assessed.