This paper presents a detailed first principles model for the energy building control with a DAE structure of index 1. The model is able to capture significant characteristics such as building temperature and air quality, which can be used to improve the control performance and the thermal comfort. The application focus of the current work is the climate control in buildings located in tropical areas, where heating is not necessary but cooling is a major issue. In this contribution, the proposed model is used in three optimization problems with different objective functions. The first objective function is the heat load associated with cooling and dehumidfying the air, the second is the thermal comfort as measured by the Predicted Mean Vote (PMV), and the third is a combination of the other two. The results for these three cases are compared for the main physical variables of the building (temperature, pressure, relative humidity) and PMV, showing that a compromise between energy efficiency and thermal comfort can be achieved.