# Why don't we call this irreversible?

I've read that a quasi-static process in which entropy change only because of heat exchange: $$\Delta S=\int \frac {\delta q} T$$ is not called irreversible. The name irreversible is reserved for processes in which work is not ideal (for example if there is friction). However these spontaneous processes are actually irreversible. So why it's not called irreversible?

• There are plenty of irreversible processes which do not even involve work. – Chet Miller Feb 25 at 14:35

This is a widespread misunderstanding, and it is based on a poor notation. The relationship between heat exchange and entropy growth is $$\Delta S \ge \int \frac{dq}{T}$$ for a general process. An equality sign is only correct here in the restricted case of reversible processes: $$\Delta S = \int \frac{dq_{\rm rev}}{T}.$$ If a heat exchange is taking place by a reversible process, then what is happening is that the heat is flowing across an infinitesimal temperature difference. In the limit that temperature difference will be zero and then the heat flow is truly reversible: the heat can then flow in either direction, and just an infinitesimal change in conditions will reverse the flow.

One often feels that heat flow is "spontaneous" and therefore irreversible, but this no more true of heat flow than it is of mechanical work when a volume changes. If there is a tiny pressure difference between two side of a friction-less barrier, then the barrier will move "spontaneously", only of course it is not so much spontaneous as dictated by the pressure difference. If that pressure difference is vanishingly small then such a process is thermodynamically reversible. Similar statements apply to heat flow when it is taking place slowly and without restriction. The word "slowly" here means that the relevant systems move through a sequence of equilibrium states so the process is called quasistatic; the phrase "without restriction" is needed to say that there is no thermally insulating barrier or something like that, which could create a temperature gradient. One can say the same thing by saying "without hysteresis". These are various different ways of expressing the same concept.

I've read that a quasi-static process in which entropy change only because of heat exchange: $$\Delta S=\int \frac {\delta q} T$$ is not called irreversible.

Only a reversible heat transfer is not irreversible. A change in entropy is defined for a reversible heat transfer, or

$$\Delta S=\int \frac{\delta q_{rev}}{T}$$

Where $$T$$ is the temperature at the boundary between the system and surroundings. Note the subscript $$_{rev}$$ for $$\delta q$$, that is missing from your equation.

Although $$\Delta S$$ is defined for a reversible process, in the case of an irreversible process between two equilibrium states one can devise any convenient reversible path between the states and apply the definition. That's because entropy is a state function independent of the path (process(s)) between the states.

However, when the process is irreversible the change in entropy consists of two parts, (1) the entropy transfer plus (2) the entropy generated due to the irreversible process, or

$$\Delta S=S_{trans}+S_{gen}$$

$$\Delta S=\int \frac{\delta q}{T}+S_{gen}$$

Where $$\delta q$$ is the differential heat transfer from the surroundings, $$T$$ is the temperature at the boundary between the system and surroundings across which heat flows, and $$S_{gen}$$ is the amount of entropy generated within the system as a result of irreversibility. $$S_{gen}=0$$ for a reversible process.

For the irreversible process we have

$$S_{gen}=\Delta S - S_{tran}=\Delta S-\int \frac {\delta q}{T}$$

The name irreversible is reserved for processes in which work is not ideal (for example if there is friction).

The name irreversible does not only apply to irreversible work. It also applies to irreversible heat transfer, i.e., heat transfer across a finite temperature difference.

However these spontaneous processes are actually irreversible. So why it's not called irreversible?

Not sure what you mean by "these" spontaneous processes. All spontaneous processes (work and heat) are irreversible and named so.

Hope this helps.