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As per my understanding, all adiabatic processes carried out in absence of an adiabatic wall need to be fast enough so that there is no heat exchange with the surrounding. Similarly, all isothermal processes are slow so that thermal equilibrium can be established with the surroundings in order to maintain a constant temperature in the system.

But then since isothermal processes are slow, how are isothermal irreversible processes possible?

Is my notion that 'irreversible processes are fast' wrong?

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There are some irreversible processes that can be slow. However, when we refer to an isothermal irreversible process, what we really mean is that the boundary of the system with its surroundings are maintained at a constant temperature during the process, even if the process is fast. So, although the temperature at the boundary is constant, the temperature distribution within the system is not spatially uniform, and irreversible heat conduction is occurring within the system. Also, typically in an isothermal irreversible process, the boundary temperature is assumed to be held at the initial uniform temperature of the system in its initial thermodynamic equilibrium state, and the temperature of the system again becomes uniform at the boundary temperature in the final equilibrium state of the system.

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  • $\begingroup$ What if I have been given that a system is such that it can exchange heat with the surroundings and there is a process that changes the state of the system and that the process is slow. Can we conclude from this information that the process must be isothermal? Also can you please give some example of an irreversible process that is slow? $\endgroup$
    – Akshat Joshi
    Commented Mar 6, 2018 at 3:55
  • $\begingroup$ An example of an arbitrarily slow and irreversible process is a gas being compressed with a piston so that there is friction with the wall. All reversible processes are "slow" where being slow is meant relative to the internal relaxation time, e.g., in a gas that is in the order of the speed of sound. This has nothing to do with being isothermal or not, and as Chester Miller pointed out that refers to the boundary conditions not what happens inside the system. If the process is reversible then isothermal is isothermal everywhere in the system, as well, but if irreversible then it may not. $\endgroup$
    – hyportnex
    Commented Mar 6, 2018 at 13:18
  • $\begingroup$ You can conclude that for a slow change of state of a pure substance, the process is isothermal. For multicomponent mixtures, this is not the case. Another example of an irreversible process that is slow is heat transfer through a wall of low thermal conductivity. $\endgroup$
    – Chet Miller
    Commented Mar 6, 2018 at 13:58
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Thermodynamics doesn't deal with rate or speed. Instead it deals only with initial state and final state, or a series of states. Mostly, it likes a very very slow process. Anything fast will generate result deviating from the thermodynamics solution.

When you talk about a fast process. It is true there is no time for heat to transfer though there still be some. However, when it is a fast movement of piston in a chamber, the gas in the chamber is not uniformly distributed, neither temperature nor concentration. There is no way you can use thermodynamics laws to get the distribution.

So, all what we said is "fast" indicates adiabatic. And it is a good approximation in real life. But don't forget we have another assumption that the internal system mixes very well, which usually needs a slow process to achieve.

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