The density of liquid carbon dioxide is about 0.8 g/cm^3. What volume fraction inside the fire extinguisher (when it is full) is occupied by liquid CO2? The density of CO2 gas is negligible compared to the density of liquid CO2. Volume of fire extinguisher is 7.1*10^-3m^3; Total mass of CO2 = 4.5 kg; T = 293K; Pressure at that temperature has to be 60*10^5 Pa.

Hmmm. PV=kT

we know that at STP,
(100kPa)(22.4L)=k(273.15K)
Under the proposed conditions above,

(60000kPa)(V')=k(293K)

V'/22.4 = (293/60000)/(273.15/100)
V' = 0.04L

So, the volume fraction is

.04/7.1 = 0.56%

I don't really think we have to worry about the mass/density of the CO2.

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%.