# Why do reversible processes not increase the entropy of the universe infinitesimally?

The book Commonly Asked Questions in Thermodynamics states:

When we refer to the passage of the system through a sequence of internal equilibrium states without the establishment of equilibrium with the surroundings this is referred to as a reversible change. An example that combines the concept of reversible change and reversible process will now be considered.

For this example, we define a system as a liquid and a vapor of a substance in equilibrium contained within a cylinder that on one circular end has a rigid immovable wall and on the other end has a piston exerting a pressure equal to the vapor pressure of the fluid at the system temperature. Energy in the form of heat is now applied to the outer surface of the metallic cylinder and the heat flows through the cylinder (owing to the relatively high thermal conductivity), increasing the liquid temperature. This results in further evaporation of the liquid and an increase in the vapor pressure. Work must be done on the piston at constant temperature to maintain the pressure. This change in the system is termed a reversible change. It can only be called a reversible process if the temperature of the substance surrounding the cylinder is at the same temperature as that of the liquid and vapor within the cylinder. This requirement arises because if the temperatures were not equal the heat flow through the walls would not be reversible, and thus, the whole process would not be reversible.

But if the system and surroundings are in fact at the same temperature then why would this process occur at all?

My understanding is that in fact that they are infinitesimally different in temperature so I guess my question is why infinitesimality gets these processes "off the hook" for being irreversible. In other words, why do these infinitesimal changes not correspond to an infinitesimal increase in the entropy of the universe, rather than none at all?

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## 3 Answers

Reversible means we can run the process reverse way without any "strangeness". Reverse the process means turn all the interactions opposite way. Lets say, in some process, you transferred out of the system 10 kJ of heat (sign of heat transferred out of the system is negative so Q=-10 kJ). Reverse the process is to transfer this 10kJ back to system from surroundings (positive sign this time).

Now, let say, the system is actually hotter than surrounding, so you transfer out this 10 kJ of heat easily (if the system has large heat capacity we can neglect the fact that it cooled slightly). But going back is a little awkward, system is still hotter and we want to "put heat" back to the system. Its just impossible. But what is potentially possible is to transfer heat back and forth (avoiding any strangeness) without any temperature difference (or infinitesimally small temperature difference - so how small is really infinitesimally small?).

My conclusion is that reversible processes are potentially attainable but not realistic (something like perfect beauty) - every real process is indeed irreversible. Yet we use it in thermodynamics as simplification of real processes, and we can obtain relatively simple mathematical equations for them.

So essentially, the discussion about realism of reversible processes are something like discussion about realism of point concept in geometry.

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Hi Martin, welcome to Physics.SE. Can you please edit your question to add some whitespace for readability? – Brandon Enright Feb 21 '14 at 0:11

The entropy of the surroundings does change infinitesimally. But the surroundings are large and such a change does not change the total entropy of the surroundings in any sensible way.

Indeed, one already uses that fact in putting the system through a series of reversible steps. As you point out, if the temperature of system and surrounding were in fact identical, no heat would flow. But they are infinitesimally different and so an infinitesimal amount of heat does flow.

The same applies to the surroundings. It too is undergoing a reversible change.

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By definition a reversible process in an isolated system cannot increase entropy. If entropy is increased during a process in an isolated system then the process is irreversible, by definition.

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