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In an isolated system with adiabatic walls in which gas is filled what exactly happens? How do we define the volume of a gas here? Is volume of 1 mole of gas present in that inelastic container the same as the volume of say 5 moles of the same gas in that container?

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  • $\begingroup$ Sure. What did you think? $\endgroup$ Commented Apr 9, 2020 at 15:10
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    $\begingroup$ By definition, gasses fill the volume of their container. $\endgroup$
    – Karsten
    Commented Apr 15, 2020 at 11:53
  • $\begingroup$ Do you think, if there were originally 5 moles and 4 moles were spent, there would be 1 mol in the 1/5 of the container volume, and rest would be vacuum ? $\endgroup$
    – Poutnik
    Commented Apr 16, 2020 at 5:32
  • $\begingroup$ @Poutnik, that would break the second law of thermodynamics 😃! $\endgroup$
    – Edison Yau
    Commented Apr 16, 2020 at 7:09
  • $\begingroup$ @Edison Yau Thinking is not bound by laws of thermodynamic. More precisily, thinking is, but its conclusions are not :-) $\endgroup$
    – Poutnik
    Commented Apr 16, 2020 at 7:12

1 Answer 1

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The volume of a gas is based on the pressure, temperature and number of moles. According to the ideal gas law :

$PV = nRT$

Where P is the pressure, V is the volume, n is the number of moles, R is a gas constant and T is the temperature.

In your case, the volume of both containers is the same, thus the volume of both gases are equal. However, assuming the temperature of the system is constant, the pressure that the gases exist must be different :

V, T, R = Constants -> $ n \propto P$

Therefore, the pressure of the container with 5 moles is five times of that of the one with 1 mole.

To actually make a fair comparison of the volumes of both moles of gases, the pressure that they are in need to be the same. So, if 5 moles of the gas is placed in a container that has 5 times the volume of the one with one mole, the pressure would be the same but the volume would be different (5:1).

Here is a helpful video for you to understand the concept: https://www.youtube.com/watch?v=BxUS1K7xu30

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