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The vapor pressure of your water column at 50 degrees C is approximately 100 Torr, which is 1/7.6 of one atmosphere. The pressure in the water column is given by the equation $P = \rho g h$ , where $\rho$ is the density of the water, g is the local acceleration due to gravity, and h is the height of the water column above a stated point. The water will ...

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The answer you are looking for is that $$\rho \propto 1/V$$ and $$m/\rho = 1/V$$ with this knowledge you should be able to see how your final equation relates to $$pV = nRT$$

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A cooled surface is your best bet. Pressure-related phenomena are also a valid choice (basically, anything that changes the properties of the air-vapour mixture into conditions above saturation is fine), or combination of both. A cooled surface must have high thermal conductivity to drain the excess latent heat that is emitted during condensation (metal is ...

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