Free expansion of a Van der Waals gas, physical explanation

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Discussion Overview

The discussion revolves around the physical explanation for the cooling effect observed during the free expansion of a Van der Waals gas, contrasting it with the behavior of an ideal gas. Participants explore the implications of intermolecular attractions and energy transformations during this process.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant notes that a Van der Waals gas cools during free expansion, unlike an ideal gas, which maintains its temperature due to unchanged internal energy.
  • Another participant suggests that the cooling can be explained by the need for heat energy from the surroundings to overcome intermolecular attractions during expansion.
  • A later reply questions the initial understanding, stating that no heat is exchanged with the surroundings during free expansion for both gas types, leading to confusion about energy changes.
  • Further contributions discuss the relationship between kinetic and potential energy, suggesting that as the gas expands, the kinetic energy decreases, which may imply an increase in potential energy due to increased distance between molecules.
  • One participant speculates that the increase in potential energy must balance the decrease in kinetic energy, leading to a lower temperature, but expresses uncertainty about this reasoning.

Areas of Agreement / Disagreement

Participants express differing views on the mechanisms behind the cooling of the Van der Waals gas during free expansion, with no consensus reached on the underlying physical principles or energy transformations involved.

Contextual Notes

Participants highlight the complexity of energy interactions, including the roles of kinetic and potential energy, but do not resolve the uncertainties regarding the implications of these interactions during free expansion.

fluidistic
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Hello!
Today I've learned that when a Van der Waals gas undergoes a free expansion, it cools down a bit. :bugeye:
This is in contrast with the ideal gas in which case since it does no work and since the process is adiabatic, the internal energy of the ideal gas remains unchanged by the expansion and since the temperature of the gas depends strictly on its internal energy, the temperature remains unchanged.
However for a Van der Waals gas, one has ##\Delta T=\frac{2an}{3R} \left ( \frac{1}{V_f} - \frac{1}{V_i} \right )##. Where a is, according to Wikipedia:
WikiTheGreat said:
a measure of the attraction between the particles
.
So the change of temperature doesn't seem to depend on the size of the gas' particles, only on the attraction between particles and the change in volume.

I don't really grasp it physically. What's going on for a Van der Waals gas during a free expansion? Why is the temperature going down?!
 
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The conceptual explanation seems straight forward to me : If there are attractions between
the gas molecules then heat energy from the surroundings will be required to overcome them
during expansion. And of course that heat will be released during compression.
 
morrobay said:
The conceptual explanation seems straight forward to me : If there are attractions between
the gas molecules then heat energy from the surroundings will be required to overcome them
during expansion. And of course that heat will be released during compression.

Ah bingo!
That makes sense, thank you.

Edit: Hmm I'm not really sure. If I'm not wrong for both the ideal and Van der Waals gas, the total energy remains unchanged, no heat is being released/absorbed from the surrounding during the free expansion and no work is done either.
I'm still at a loss.
 
Imagine there is no change in internal energy (as the gas can expand into a vacuum in an adiabatic bath).

Consider the interplay between kinetic and potential energy of the gas.
 
Jorriss said:
Imagine there is no change in internal energy (as the gas can expand into a vacuum in an adiabatic bath).
Yeah I noticed.
Joriss said:
Consider the interplay between kinetic and potential energy of the gas.

Hmm I'm not sure at all.
Apparently the kinetic energy decreases because the temperature decreases during the expansion? This would mean that the potential energy increases (is is the enthalpy?). But I don't get really understand why this happens.
Ah.. I think it's because the molecules are getting farther away from each other so the potential energy of "attraction" between the molecules increases. Since the total energy must remain constant, this means that the kinetic energy has to lower, and hence the temperature.
Does that sound correct?
 

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