Maxwell's Demon and Irreversible Ideal Gas Expansion?
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2025
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| _version_ | 1866902027963990016 |
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| author | Ruggeri, Francesco R. |
| author_facet | Ruggeri, Francesco R. |
| contents | <p dir="ltr"> In (1), a single particle (which represents an ideal gas) is present in a container of volume V coupled presumably to a reservoir at temperature T. A Maxwell demon knows the position of the particle and inserts a partition in the middle of the container when the particle is near the left hand wall. The particle then isothermally pushes the partition to the right hand wall and the system is back to its initial state (claim). Heat from the reservoir has been converted entirely into work violating the second law of thermodynamics.</p> <p dir="ltr"> Here we argue that placing a partition at V/2 when the original state was V already violates the second law of thermodynamics because the entropy changes from C1 ln(V) to C1 ln(V/2), i.e. the system becomes more ordered with no effort. In a previous note (2), we have made a similar argument, namely that if the particle, representing an ideal gas, was originally in V and is now in V/2, then work must have been done to push it into V/2 isothermally. Then there is no issue with it expanding back to its original state (see (2)).</p> <p dir="ltr"> Here we argue that the instant the demon places a participation at V/2, the starting volume is V/2 and the spatial entropy ln(V/2). We suggest that in order to not violate the second law of entropy, one may treat this problem as having an initial state of V/2 and analyzing from that point on because the sudden change from V to V/2 is not consistent with the second law.</p> <p dir="ltr"> Thus, heat from the reservoir matches the isothermal work, but there is an increase in entropy as the particle ( or gas) moves from V/2 to V. In such a case there is no violation of the second law of thermodynamics. We argue that this is the quasistatic path equivalent to an irreversible expansion of an ideal gas. The overall effect is an increase in entropy in the gas which does not violate the second law of thermodynamics</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15381184 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Maxwell's Demon and Irreversible Ideal Gas Expansion? Ruggeri, Francesco R. <p dir="ltr"> In (1), a single particle (which represents an ideal gas) is present in a container of volume V coupled presumably to a reservoir at temperature T. A Maxwell demon knows the position of the particle and inserts a partition in the middle of the container when the particle is near the left hand wall. The particle then isothermally pushes the partition to the right hand wall and the system is back to its initial state (claim). Heat from the reservoir has been converted entirely into work violating the second law of thermodynamics.</p> <p dir="ltr"> Here we argue that placing a partition at V/2 when the original state was V already violates the second law of thermodynamics because the entropy changes from C1 ln(V) to C1 ln(V/2), i.e. the system becomes more ordered with no effort. In a previous note (2), we have made a similar argument, namely that if the particle, representing an ideal gas, was originally in V and is now in V/2, then work must have been done to push it into V/2 isothermally. Then there is no issue with it expanding back to its original state (see (2)).</p> <p dir="ltr"> Here we argue that the instant the demon places a participation at V/2, the starting volume is V/2 and the spatial entropy ln(V/2). We suggest that in order to not violate the second law of entropy, one may treat this problem as having an initial state of V/2 and analyzing from that point on because the sudden change from V to V/2 is not consistent with the second law.</p> <p dir="ltr"> Thus, heat from the reservoir matches the isothermal work, but there is an increase in entropy as the particle ( or gas) moves from V/2 to V. In such a case there is no violation of the second law of thermodynamics. We argue that this is the quasistatic path equivalent to an irreversible expansion of an ideal gas. The overall effect is an increase in entropy in the gas which does not violate the second law of thermodynamics</p> |
| title | Maxwell's Demon and Irreversible Ideal Gas Expansion? |
| url | https://doi.org/10.5281/zenodo.15381184 |