Combining Differently-Tempered Gases: Calculating Internal Energy Change

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To combine two separate volumes of an ideal gas at different temperatures, pressures, and volumes, one must consider the total energy of each chamber, which includes both potential and kinetic energy. The total energy can be calculated by summing the energies of each individual system. In a closed system with a barrier, the interaction between the two volumes will depend on whether the barrier is flexible or if a valve is opened. Regardless of the interaction method, the total energy can be determined by combining the energies of both chambers. This approach assumes no external influences on the system.
winstonsmith
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How do you combine two separate volumes of an ideal gas which are at different temperatures pressures and volumes and then work out the change in internal energy?
I have been trying to get my head around this without success.
 
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It has been a while since I used this, but:

total energy (T)=potential energy (P)+ kinetic energy (K)
I forgot the actually variable symbology you are probably using.

T1=P1+K1; T2=P2+K2
Tcombined= P1+P2+K1+K2

that simple I think.

If your asking how would you combine the volums of gas it would probably depend on what type of experiment you are doing and the type on energy in the system you are trying to analyze.
 
Thanks.
I am considering a closed system that contains two different sized chambers chambers separated by a barrier each chamber has the same ideal gas in different volumes, temperature and pressure.
 
winstonsmith said:
Thanks.
I am considering a closed system that contains two different sized chambers chambers separated by a barrier each chamber has the same ideal gas in different volumes, temperature and pressure.


How will the two volums interact? will you open a valve of is the plate separating them flexible? Actually, it probably doesn't matter. Simple calculate the total energy of each system and combine them for the total evergy of all systems. If you are assuming no interaction with outside world, then this will work. even if you have a negative pressure and a positive pressure that are equal in magnitude (and all the other variables are equal) you might think the total energy should be zero, and it should, since one will have negative pressure and the other positive pressure. All the energy of each system would be release by the transfer.
 
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