# Reversibility and isothermal processes

I would like to know why any reversible process has to be isothermal, according to my sources.

Why can´t we consider adiabatic processes to be reversible?

EDITED

https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter5.html (In "Mechanical and thermal reversibility" section)

For summing up, this text says that any reversible process has to be constantly in thermodynamical equilibrium and frictionless (No problem until this point). But later on, it claims that has to be isothermal too, what is a more restrictive condition than to be in thermal equilibrium (if isothermal, the process is in thermal equilibrium, but the converse is not true)

Why this another condition, is there any intuitive explanation?

• reversibility means if the system is in equilibrium with itself, i.e. pressure is same everywhere in container etc..also rewrite the question for better understanding – Mrigank Feb 24 '16 at 21:40
• Do you say that the only requirement for a process to be reversible is the homogeneity of its intensive state variables (pressure and temperature)? – amejmar Feb 24 '16 at 22:45
• A reversible process does not have to be isothermal. Adiabatic processes can also be reversible. And then there are an infinite array of reversible processes that are neither isothermal nor adiabatic. If your source says that a reversible process has to be isothermal, it's wrong (or you mis-interpreted what it is saying). – Chet Miller Feb 24 '16 at 23:42
• When they (incorrectly) say that All Heat Transfer is Isothermal, what they really mean is that, throughout the process, the surroundings differ in temperature from the system only slightly; however, the difference is enough for the system temperature to be changing very gradually during the process. So if the system is being heated by the surroundings, the surroundings temperature is always slightly higher than the system temperature (throughout the change). Of course, in an adiabatic process, there is no heat transfer. – Chet Miller Feb 24 '16 at 23:58
• @amejmar yes, at every point of time during process – Mrigank Feb 25 '16 at 16:01

This is what it says on the linked page:

...thermal reversibility requires that all heat transfer is isothermal.

This statement is only true in the context of that web-page, where it is being assumed that the system is in contact with a thermal reservoir (i.e. an object whose thermal mass is so large that it's temperature doesn't change while exchanging energy via heat with the system).

We know that a process in which there is energy transfer via heat between two objects at different temperatures is irreversible, and so in order for a process to be reversible in this context, the system and the environment must be at the same temperature at all times during the heat transfer. Since the environment's temperature doesn't change, neither can the system's.

Thus:

A reversible process in which energy is exchanged via heat between a finite system and an infinite reservoir must be isothermal.

Now, it is possible to design a reversible process in which the system's temperature changes and the system exchanges energy via heat with its environment. If you bring a system into contact with a sequence of thermal reservoirs, each at an infinitesimally larger temperature than the last, and you allow the system and reservoir to equilibrate at each step, then the system gains energy via heat, and its temperature goes up. Crucially, this heat exchange occurs when the system is in contact with a reservoir at the same temperature, so the entire process is reversible.

Only condition is all the changes must be infinitesmal, this is the only way to keep intensive variables (most importantly, temperature and pressure) homogeneous during every point of time during process like you said, and I think you misinterpreted isothermal, by isothermal, it should mean that difference between system and surrounding temperature must be infinitesmal, it doesn't have anything to do with the kind of process we are performing, to set up adiabetic reversible,just put surroundings at exact same temperature as system {at every point of time during the process} , since no temperature difference, no heat will flow and the condition of process is fulfilled or simply using an isolated system would be more than enough, with other systems also like a piston having infinitesmal pressure difference only for the reasons mentioned above.