The total volume of the can \(V_{\mathrm{can}}\) is 0.375 L, and the initial volume of liquid in the can \(V_0^\ell\) is:

\[ V_0^\ell = f\,V_{\mathrm{can}}, \]

where \(f\) 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 \(P^{\mathrm{sat}}\) at 300 K. The Antoine equation is used to calculate \(P^{\mathrm{sat}}\):

\[ P^{\mathrm{sat}} = 10^{A - \frac{B}{\mathrm{T_c} + C}}, \]

where \(P^{\mathrm{sat}}\) is in bar, \(T_{\mathrm{c}}\) is temperature (°C), and \(A, B, C\) are Antoine constants. The total moles \(n\) are equal to the liquid moles \(n^\ell\) plus the vapor moles \(n^v\):

\[ n = n^\ell + n^v,\quad n^\ell = \rho^\ell\,V^\ell,\quad n^v = \frac{P^{\mathrm{sat}}\,V^v}{R\,T}, \]

where \(\rho^\ell\) is the liquid molar density (mol/L), \(R\) is the ideal‐gas constant (L·bar/(mol·K)), \(T\) is the absolute temperature (K), and \(V^\ell\) and \(V^v\) are the liquid and vapor volumes at any time. The liquid volume is found by rearranging the total‐moles equation:

\[ V^\ell = \frac{n - \dfrac{P\,V_{\mathrm{can}}}{R\,T}}{\rho^\ell - \dfrac{P}{R\,T}}, \quad V^v = V_{\mathrm{can}} - V^\ell. \]

From an unsteady‐state mole balance:

\[ \frac{dn}{dt} = -\alpha\,(P^{\mathrm{sat}} - 1), \]

at \(t=0\), \(n = n_0\); where \(\alpha\) is a constant (mol/(bar·s)) and the outside air pressure is 1 bar.

From the energy balance:

\[ \frac{dT}{dt} = -\frac{\Delta H_{\mathrm{vap}}}{n\,C_p}\,\frac{dn}{dt}, \]

at \(t=0\), \(T = 300\) K, where \(\Delta H_{\mathrm{vap}}\) is the heat of vaporization (kJ/mol), and \(C_p\) is the liquid heat capacity (kJ/(mol·K)).

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. 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". Set the time the spray stops with a slider. 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.

This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by Sneha Nagaraju under the direction of Professor John L. Falconer and Michelle Medlin. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael Bauman. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.