A glass bulb with radius 15cm is filled with water vapor at a temperature of 500K. On the exterior of the bulb, a spot with area 2.0mm$2$ is placed in contact with liquid nitrogen. This causes the temperature of the spot to drop well below 0 degrees C. When the gaseous water molecules strike this area from inside, they immediately freeze, effectively removing them from the gas. 

Determine how much time it takes for the pressure in the bulb to reduce to half its original value. Assume the temperature of the gas in the container remains at 500K.

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