Answer:
The thermal energy of an energy system that has been contained within a polystyrene cup is dissipated to the surroundings when the system cools down to room temperature. Specifically, thermal energy is transferred from the system to its surroundings through the process of heat transfer. This heat transfer happens due to the temperature difference between the system and its surroundings, which drive the flow of thermal energy from the hot region (the system) to the cooler region (the surroundings) until equilibrium is reached.
The main mechanism of heat transfer in this context is conduction, which occurs as a result of molecular collisions at the interface between the system and its surroundings. Additionally, heat transfer can also occur through processes like convection, where fluids or gases carrying energy are moved by external forces, and radiation, which involves emission and absorption of electromagnetic waves. In summary, the thermal energy of an energy system that has cooled down to room temperature is lost to its surroundings through the transfer of heat, mainly via conduction.