Adiabatic Evaporation of Water into Vacuum

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In this Demonstration, a cylinder fitted with a weightless, frictionless piston initially contains a liquid slightly above its saturation pressure; the volume above the piston is initially under vacuum. You can select the initial mass and temperature of the liquid using the sliders. The final volume is fixed at 1.0 L. Expansion is enabled when the orange stop is removed. The piston then moves to the top of the cylinder as some liquid evaporates, resulting in the final values of temperature, pressure and liquid mass, as shown. The temperature drops due to evaporative cooling, while the final pressure reaches its saturation value.

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Use the "reset" button to start again.

The liquid volume in the cylinder is exaggerated relative to the vapor volume for better visualization.

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Contributed by: Neil Hendren (March 25)
With additional contributions by: John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)

Open content licensed under CC BY-NC-SA


Details

For an initial mass and temperature of liquid water, the total internal energy is:

, (1)

where is the initial specific internal energy of the liquid. The internal energy is zero at 0° C. The piston is weightless and water evaporates into a vacuum, so no work is done. Since the system is adiabatic, is constant. The mass balance and energy balances for the system are:

, (2)

, (3)

where is final mass of liquid, is the final mass of vapor, is the final specific internal energy of the liquid and is the final specific internal energy of the vapor.

The total volume of the cylinder is 1 L; is related to the final specific volumes of the saturated vapor () and liquid ():

. (4)

Published steam tables are used to solve for the final temperature and the final amount of liquid.


Snapshots



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