To find the volume fraction of liquid carbon dioxide inside the fire extinguisher, we need to calculate the volume occupied by the liquid CO2 and divide it by the total volume of the fire extinguisher.
First, we need to convert the given values to their corresponding SI units:
Density of liquid carbon dioxide = 0.8 g/cm^3 = 800 kg/m^3
Volume of fire extinguisher = 7.1 * 10^-3 m^3
Total mass of CO2 = 4.5 kg
Temperature (T) = 293 K
Pressure (P) = 60 * 10^5 Pa
Using the ideal gas law, we can determine the volume of CO2 gas:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the gas
n = Number of moles of the gas
R = Universal gas constant
T = Temperature
Rearranging the equation to solve for V:
V = (nRT) / P
To find the number of moles (n) of CO2 gas, we use the mass of CO2 and its molar mass (44 g/mol):
n = mass / molar mass
n = 4.5 kg / (44 g/mol)
n = 4.5 kg / 0.044 kg/mol
n = 102.27 mol
Using the value of n and the given values of P and T, we can calculate the volume of CO2 gas:
V = (102.27 mol * 8.314 J/(mol·K) * 293 K) / (60 * 10^5 Pa)
V = 0.167 m^3
Now, we can calculate the volume fraction of liquid CO2:
Volume fraction of liquid CO2 = Volume of liquid CO2 / Total volume of the fire extinguisher
Volume of liquid CO2 = Total volume of the fire extinguisher - Volume of CO2 gas
Volume of liquid CO2 = 7.1 * 10^-3 m^3 - 0.167 m^3
Volume of liquid CO2 = 6.933 * 10^-3 m^3
Volume fraction of liquid CO2 = (6.933 * 10^-3 m^3) / (7.1 * 10^-3 m^3)
Volume fraction of liquid CO2 = 0.977
Therefore, the volume fraction inside the fire extinguisher occupied by liquid CO2 when it is full is approximately 0.977, or 97.7%.