It is shown that the RHIC energy-scan experiments can serve as an effective tool for studying the system evolution along the first order phase transition line passing the critical point, which is a second order phase transition process. During this process the system structure changes while passing the critical point, and correspondingly, the transverse momentum of the final state particles gets an extra component. This phenomenon can provide useful information about the system structure in different phases and can serve as an effective signal for locating the critical point.