Combining Differently-Tempered Gases: Calculating Internal Energy Change

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Discussion Overview

The discussion revolves around the calculation of the change in internal energy when combining two separate volumes of an ideal gas at different temperatures, pressures, and volumes. The context includes considerations of a closed system and the interactions between the gas volumes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant inquires about the method to combine two volumes of ideal gas with differing temperatures, pressures, and volumes to determine the change in internal energy.
  • Another participant suggests a formula for total energy that includes potential and kinetic energy but does not specify the variables used in the context of gases.
  • A participant clarifies that they are considering a closed system with two chambers containing the same ideal gas but differing in volume, temperature, and pressure.
  • Further discussion raises questions about how the two volumes will interact, mentioning the possibility of opening a valve or having a flexible barrier, though it is suggested that the method of interaction may not significantly affect the energy calculations.
  • There is a mention of calculating the total energy of each system and combining them, with a note on the implications of having equal but opposite pressures in the chambers.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the method for calculating the change in internal energy, and multiple viewpoints regarding the interaction of the gas volumes and energy calculations remain present.

Contextual Notes

The discussion includes assumptions about the nature of the gas interactions and the definition of energy types, which are not fully resolved. There is also ambiguity regarding the impact of pressure differences on total energy calculations.

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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