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.

Question

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.

Steve · Answer

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.