An insulated container contains two chambers of equal volume separated by a rigid wall. One chamber holds 2 kg of gaseous O2 at 100 kPa and 310 K. The other chamber is completely evacuated. The wall is then removed, and the O2 fills both chambers and is allowed to come to equilibrium. What is the final temperature?

Final Temperature is 310K

Explanation:

Given that:

Mass of O₂ gas = 2 kg

Pressure (P₁) = 100 kpa

Temperature (T₁) = 310K

We also have, ΔQ = ΔU + ΔW where ΔQ is the heat transferred into/out of the system, ΔW is the work done and  ΔU is the change in internal energy of the system.

As soon as the wall is removed, the process called expansion process allows the evacuated chamber to be filled. Work done ΔW = PdV = 0, this is because P the external  pressure against which the gas is expanding is zero, therefore the work done is zero.  

ΔU which is highly dependent on the temperature is zero since there is no heat transferred in or out of the container due to it being insulated. This therefore means that the initial temperature is the same as the final temperature when the container if filled completely.

T₁ = Final temperature = 310 K

The final Temperature is therefore 310K