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According to Wikipedia, a reversible process is "a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, with no increase in entropy."

However, for isothermal processes, any reversible heat added to the system at constant temperature increases entropy. So, a reversible process of heating is causing a change in entropy. This seems to contradict the definition above.

Where have I gone wrong?

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The entropy does not change if the process is reversible and the system is closed. In your example you are taking into account only the subsystem which indeed has its entropy increased. If you consider also the neighbourhood then you see that its entropy change is negative (loosing heat) and that precisely cancels the entropy change of the subsystem. The entropy of the whole closed system does not change.

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  • $\begingroup$ What do you mean by neighborhood? $\endgroup$ – sangstar Dec 2 '17 at 21:29
  • $\begingroup$ @sangstar everything that is exchanging heat with your system. $\endgroup$ – Diracology Dec 2 '17 at 21:39
  • $\begingroup$ Could you give a physical example? I'm having trouble understanding it from that definition. $\endgroup$ – sangstar Dec 2 '17 at 21:42
  • $\begingroup$ @sangstar a heat engine under Carnot cycle. The gas is the system whereas the hot and cold thermal reservoirs (sources) form the neighbourhood. Another example: the system you mentioned. It gain heat isothermically. Well something has to be losing heat. That is the neighbourhood. $\endgroup$ – Diracology Dec 2 '17 at 21:46
  • $\begingroup$ The hot and cold sources form the neighborhood? But how can their entropy change be negative? I thought they were thermal reservoirs, so their temperature can't change. $\endgroup$ – sangstar Dec 2 '17 at 22:24

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