Substance evaporation temperature

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A substance can only evaporate at its saturation temperature (T(sat)) for a given pressure because evaporation requires the vapor pressure to equal the ambient pressure. When a pressurized container is opened, the pressure drops, leading to a decrease in T(sat), which allows the substance to evaporate at that new temperature. Evaporation occurs until thermal equilibrium is reached, cooling the surface as it transitions from liquid to vapor. Higher temperatures do not facilitate evaporation at the original pressure because the vapor pressure must match the external pressure for the process to occur. Understanding these principles is crucial for applications involving phase changes, such as refrigeration.
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Can a substance only evaporate at the T(sat) at that particular pressure and why not even at a higher temperature?
Example of a refrigerant at room temperature, pressurized container. But when it's opened, the P falls and T(sat) falls, so it goes to that T(sat) temperature to evaporate. But why? Why not evaporate at the room temperature itself?
 
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Evaporation reduces the temperature of the surface until you have an equilibrium (or something close to it) at the surface.
 

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