No, the dew point of a room cannot exceed the temperature of the room (θᵣ) if there is already water in liquid form at that temperature. The dew point is the temperature at which air becomes saturated with water vapor and starts to condense into liquid form. It represents the point at which the air cannot hold any more moisture and begins to release it.
When the temperature of the room is equal to the dew point, the air is saturated with water vapor, and any further decrease in temperature will cause condensation to occur. Therefore, if there is already liquid water present in the room at the given room temperature, it indicates that the air is already at or below its dew point. In this situation, the dew point cannot exceed the temperature of the room.
It's important to note that if the temperature of the room decreases further below its initial temperature, additional condensation may occur as the air becomes even more saturated with water vapor. However, this does not change the fact that the initial liquid water present in the room indicates that the air was already at or below its dew point.