By free expansion, I am referring to gas kept in a piston-cylinder arrangement freely allowed to expand against vacuum.

It is clear to me that free expansion is an irreversible process because if it were not then it could get compressed as well at equilibrium, but we know it doesn't as it would be violating the 2nd law of thermodynamics.

I know that all the parameters work 'W', Change in Internal Energy '∆U', and Heat transfer '∆Q' would all be zero in the case of an ideal gas.

But, what I want to know is how will all the parameters vary if gas is real?

Also, I wanted to ask whether the answer will change if the surface between the piston and cylinder is not frictionless?

  • 2
    $\begingroup$ This is a duplicate of the same question that has been answered in Physicsstackexchange. $\endgroup$ Commented Jan 15, 2021 at 18:09
  • $\begingroup$ I asked it here as well because there are only few people who are active both on Chem and Physics SE. $\endgroup$ Commented Jan 16, 2021 at 6:24
  • $\begingroup$ Also, I wanted to see both viewpoints from chemistry and physics as thermodynamics is one topic that is common to both to a large extent. $\endgroup$ Commented Jan 16, 2021 at 6:26
  • $\begingroup$ I read the wikipedia article. But I think my problem pertains more to Joule Expansion. $\endgroup$ Commented Jan 16, 2021 at 11:06
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    $\begingroup$ Joule expansion and J.-T, effect are about the same phenomena. The system with a piston with friction will be like an irreversible adiabatic expansion Delta U = -W, So all gases would cool down, unless friction was really tiny.. BTW, put the elaboration info rather to the question. $\endgroup$
    – Poutnik
    Commented Jan 16, 2021 at 11:26

1 Answer 1


For a real gas, the internal energy varies with both temperature and molar volume. The variation is described by the equation: $$\mathrm dU=C_V\,\mathrm dT-\left[P-T\left(\frac{\partial P}{\partial T}\right)_V\right]\mathrm dV,$$ where $U$ is the internal energy per mole and $V$ is the molar volume. This means that, unless the equation of state is such that pressure is directly proportional to temperature at constant molar volume (like an ideal gas), the internal energy will depend on molar volume.

  • $\begingroup$ But isn't free expansion an irreversible process? Then how are we using differentials? Also, how can we have an equation of state for it? $\endgroup$ Commented Jan 17, 2021 at 7:22
  • $\begingroup$ I read that we can only define state variables when the system is at equilibrium. $\endgroup$ Commented Jan 17, 2021 at 7:25
  • $\begingroup$ Also will the change in enthalpy be zero in case of real gas? $\endgroup$ Commented Jan 17, 2021 at 7:34

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