One kilogram of air, initially at 5 bar, 350 K, and 3kg of carbon dioxide (CO2),

Question

One kilogram of air, initially at 5 bar, 350 K, and 3kg of carbon dioxide (CO2), initially at 2 bar, 450 K,
are confined to opposite sides of a rigid, well-insulated contained, as illustrated in the figure below.
The partition is free to move and allows conduction from one gas to the other without energy
storage in the partition itself. The air and carbon dioxide each behave as ideal gases. Determine the
final equilibrium temperature, in K, and the final pressure, in bar, assuming constant specific heats.

Explanation / Answer

m1air=1Kg P1air=5bar T1air=350K (air)

m1co2=3kg P1co2= 2bar T1co2=450K

from property table:

Cv,air=0.726 kJ/(kg.K); Cv,CO2=0.750 kJ/(kg.K); Cp,air=1.013 kJ/(kg.K); Cp,CO2=0.939 kJ/(kg.K)

equillibrium temp:

Tf=(m,co2.Cv,co2.Tco2,i+m,air.Cv,air.Tair,i)/(m,co2.Cv,co2+m,air.Cv,air)

=(1012.5+254.1)/(2.25+0.726)=425.6K

V,tank=m,co2(R,co2.Tco2,i/P,co2)+m,air(R,air,T,air/Pair)=3(0.1889x450/2)+1(0.2870x350/5)

=127.5+20.09=147.59 litre

Pf=(Tf/Vtank)(m,co2.Rco2+m,air.R,air)=(425.6/147.59)(0.5667+0.287)=2.46bar

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