No, water does not travel faster from a hot pan at a certain temperature. The rate at which water evaporates from a pan is primarily determined by the temperature of the water, not the pan itself. When water is heated, its molecules gain energy and move more rapidly, increasing the rate of evaporation. However, the speed at which water molecules escape into the air depends on factors such as the surface area of the liquid, the humidity of the surrounding air, and the air temperature.
In a hot pan, the water molecules near the surface gain energy and escape into the air as vapor, but this process is not directly related to the speed at which the water "travels." Water molecules do not move as a coherent body; instead, they move randomly, colliding with each other and with the pan's surface. The evaporation process is a result of the random kinetic motion of water molecules, not a directed flow or travel.
It's important to note that while hotter temperatures generally increase the rate of evaporation, there are other factors at play. For example, if the air surrounding the pan is already saturated with water vapor, the rate of evaporation will slow down since there is less capacity for additional water vapor. Additionally, factors such as air movement and humidity can affect the rate of evaporation.