Why is internal energy independent of volume for an ideal gas?

isochoric/isometric:
isothermal:
isobaric:

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Harjas Sabharwal 1G
Posts: 42
Joined: Sat Jul 22, 2017 3:01 am

Why is internal energy independent of volume for an ideal gas?

Postby Harjas Sabharwal 1G » Wed Jan 24, 2018 7:29 pm

Why is internal energy independent of volume for an ideal gas?

Amanda Wu 2C
Posts: 31
Joined: Sat Jul 22, 2017 3:00 am

Re: Why is internal energy independent of volume for an ideal gas?

Postby Amanda Wu 2C » Wed Jan 24, 2018 8:07 pm

I think the reasoning behind why the internal energy of an ideal gas is independent of volume is best understood through Gay-Lussac's Joule experiment:

Simply put, the experiment consisted of two containers, one of which contained an ideal gas and one of which was completely evacuated, connected to each other by a pipe and a valve. In addition, this system is insulated from its surroundings (isolated system). When the valve was opened, the ideal gas expanded into the evacuated chamber, causing a change in pressure and volume, but no change in temperature. Because the system is isolated from its surroundings (q=0) and free expansion occurred (w=0), the internal energy of the system does not change (delta u=0). Therefore, the internal energy of the ideal gas must be attributed only to its temperature.

In short, from my understanding of this experiment, the reasoning as to why internal energy is independent of volume for an ideal gas is because in the experiment, pressure and volume changed (while the temperature remained constant), but did not cause a change in the internal energy, a change in internal energy must be dependent solely on temperature.


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