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 .

From an unsteady-state mole balance:

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.