The density of liquid carbon dioxide is about 0.8 g/cm^3. What volume fraction inside the fire extinguisher (when full) is occupied by CO2? The density of CO2 gas is negligible compared to the density of liquid CO2.
My answer was 75%. Please verify. Thanks.
V (fire extinguisher) = 7.1*10^-3 m^3
Mass CO2 = 4.5 kg
T =293 K
Pressure = 60*10^5 Pa
V(co2) = (4500g/0.8g) * 1cm^3=5625 cm^3
V(co2)/Vex = 5625/7.1*10^3 = 0.79 = 79%.
To determine the volume fraction of CO2 inside the fire extinguisher when it is full, we need to consider the densities of both the liquid CO2 and the overall mixture.
First, let's calculate the density of the mixture. Since the density of gaseous CO2 is negligible compared to the density of liquid CO2, we can assume that the density of the mixture is approximately equal to the density of the liquid CO2.
Given: Density of liquid CO2 = 0.8 g/cm^3
Next, let's express the volume fraction of CO2 as a fraction of the total volume occupied by the mixture. Let's assume that the volume of the fire extinguisher is 1 cm^3 (for easier calculation, as the volume units will cancel out).
To find the volume of CO2 gas in the fire extinguisher, we need to subtract the volume of the liquid CO2 from the total volume:
Volume of CO2 gas = Total volume - Volume of liquid CO2
Since the density is mass per unit volume, we can assume that 0.8 g of liquid CO2 occupies 1 cm^3 of volume (density = mass/volume).
Thus, the mass of liquid CO2 would also be 0.8 g when the fire extinguisher is full. Therefore, the remaining mass of the mixture (CO2 gas) would also be 0.8 g when the extinguisher is full.
Now, we can calculate the volume of CO2 gas using the known density of CO2 gas:
Density of CO2 gas = Mass of CO2 gas / Volume of CO2 gas
Since the density of CO2 gas is negligible, we can assume that the mass of CO2 gas is equal to the mass of the mixture:
Mass of CO2 gas = Mass of mixture = 0.8 g
Substituting the known values into the density equation and rearranging, we can solve for the volume of CO2 gas:
Volume of CO2 gas = Mass of CO2 gas / Density of CO2 gas = 0.8 g / 0.8 g/cm^3 = 1 cm^3
Now, we can calculate the volume fraction of CO2 gas by dividing the volume of CO2 gas by the total volume:
Volume fraction of CO2 gas = Volume of CO2 gas / Total volume = 1 cm^3 / 1 cm^3 = 1
Finally, to express the volume fraction as a percentage, we multiply by 100:
Volume fraction of CO2 gas = 1 * 100% = 100%
Therefore, the correct answer is that when the fire extinguisher is full, the volume fraction occupied by CO2 is 100%, not 75%.