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# Compressed-Gas Spray

Compressed-gas dusters spray a gas such as difluoroethane (DFE) to remove dust from electronics. When gas exits the valve, liquid DFE in the container vaporizes to maintain vapor-liquid equilibrium. The energy to vaporize the liquid is obtained by cooling the remaining liquid; the container is modeled as adiabatic in this Demonstration. Decreasing the liquid temperature decreases its saturation pressure, which lowers the driving force, and thus the gas flow rate decreases. For smaller initial volume fractions of liquid (change with a slider), the liquid cools faster.
Select a plot (volume, moles, temperature or pressure) with buttons to display how that property changes with time. Animate the duster by clicking the play button next to "spray gas". Select "stop at " and the spray will stop once is reached; or set the time the spray stops with a slider. In either case, the black dot(s) show the conditions of the duster on the plot. The liquid and vapor DFE are assumed to be in equilibrium at all times. As the spray time increases, the adiabatic approximation becomes less accurate.

### DETAILS

The total volume of the can is 0.375 L, and the initial volume of liquid in the can is:
,
where is the initial volume fraction of liquid.
Initially all contents are at room temperature (300 K), and the pressure inside the can is the saturation pressure at 300 K. The Antoine equation is used to calculate :
,
where is in bar, is temperature (K) and , and are Antoine constants.
The total moles are equal to the liquid moles plus the vapor moles :
,
,
,
where is the liquid molar density (mol/L), is the ideal gas constant ([L bar]/[mol K]), and and are the liquid and vapor volumes at any time.
The liquid volume is found by rearranging the equation for total moles:
,
with .
at , ,
where is time (s), is a constant (mol/[bar s]) and the air pressure outside of the can is 1 bar.
From the energy balance:
at , , where is the heat of vaporization (kJ/mol), and is the liquid heat capacity (kJ/[mol K]).
The screencast video at [1] shows how to use this Demonstration.
Reference
[1] Compressed-Gas Spray [Video]. (Aug 31, 2016) www.colorado.edu/learncheme/thermodynamics/CompressedGasSray.html.

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