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When water goes from gas to liquid it undergoes a phase change which requires a lot more energy than just a temperature change. When steam hits your skin, a lot of energy will be released as it condenses. This energy causes a much worse burn than if the same amount of boiling water were to hit your skin.
It helps for me to understand why steam burns more than liquid water if I remember the graph he showed us in class. I think everyone else did a fantastic job already of explaining it, but when dealing with the phase changes, at least for me, it helped seeing the comparison of energy change water underwent from vapor to liquid compared to that of liquid alone. If you can see how (for water) there is more energy required for this phase change, it makes sense why the burn is more severe.
Although steam and water may both be at 100 degrees C, the steam will give you more of a burn. Both steam and water will want to reach an equilibrium with whatever is being burned, eventually reaching 25 degrees. However, the energy given off by steam on its way to this temperature is much greater than that of water. This is because steam has much more energy per molecule than water.
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