Concerning T07.3(b)

For a given real gas, with known equation of state, we obtained an expression for its internal energy, U(T,V). The only unknown part in this expression is U(T,V_0). So now, we consider the limit V_0 to infty. Then the physical question arises, what happens to U(T,V_0) which is the internal energy of the real gas, if V_0 goes to infinity. Has anybody found an answer?

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  1. Marco29 de abril de 2020 a las 5:18 p.m.

    My first intuition was that, because for a real gas when V→∞, the pressure p→0 then the system should enter some sort of state of minimal energy for a given temperature, which might or might not be zero because of the kinetic energy of the particles.

    But then, because the velocities of the particles form some sort of distribution dependant on only temperature(?), basically a set of free particles, then the system must be congruent with the ideal gas.

    So U(T,∞) must be the internal energy of the ideal gas U_0=aT

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  2. Thomas29 de abril de 2020 a las 6:36 p.m.

    Very good! Exactly. Since the volume goes to infinity, the density goes to zero. And the distances between the particles become too large for the interaction to have any effect

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