What is the relative humidity if the dry bulb and wet bulb readings are the same?

The reading of a wet thermometer is usually lower than that of a dry thermometer, because moisture evaporates from its surface and due to this it cools. If there is no difference in the readings of dry and wet bulb thermometers, then this means that there is no evaporation and no cooling occurs. More precisely, a dynamic equilibrium has been established between evaporation and condensation. The reason is that the air is already saturated with water vapor and the evaporation is compensated by condensation. Conclusion: the relative humidity is 100%.
Answer: 100%.

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