# Thermodynamics: Why must a reversible process be infenetesimally done?

• Nikitin
In summary, a reversible process must be done infinitesimally slowly so that the system remains arbitrarily close to thermodynamic equilibrium throughout the process. This ensures that any infinitesimal changes in conditions will reverse the direction of the process. This is necessary for a process to be truly reversible, meaning that it can be reversed without materially changing any property of the system or surroundings.
Nikitin
So my professor keeps bringing up that a reversible process must always be done infinitesimally slowly up. But why is that? I can't recall the explanation.

Nikitin said:
So my professor keeps bringing up that a reversible process must always be done infinitesimally slowly up. But why is that? I can't recall the explanation.
The process has to be done slowly enough that the system is arbitrarily close to thermodynamic equilibrium during the process. If that is the case, an arbitrarily small change in conditions will cause the process to reverse direction.

If the process involves heat transfer between the system and surroundings it has to be done with an infinitessimal temperature difference between the system and surroundings (so that an infinitessimal change in temperature willl cause the heat flow direction to reverse). This effectively means that the heat transfer will take an arbitrarily long time.

If it is an adiabatic process, an arbitrarily small change in the pressure of the surroundings will result in a change in the direction of the process. This means that the net pressure on or by the surroundings (Psurr - Psys) has to be arbitrarily close to 0 so it will proceed at an infinitessimally slow pace.

AM

1 person
So the point is the system must never leave thermodynamic equilibrium during a reversible process? Why is that the case?

Nikitin said:
So the point is the system must never leave thermodynamic equilibrium during a reversible process? Why is that the case?
It must be arbitrarily close to thermodynamic equilibrium so that an infinitesimal change in conditions will reverse the direction of the process. This is what we mean by a reversible process.

AM

Could you please explain it less formally, and more intuitively?Sent from my iPhone using Physics Forums

Intuitively, if the system is taken away from equilibrium there will be irreversible internal process that would eventually re-establish equilibrium. Take the example of a hot object in contact with a cold one. Heat always flow from the warm one to the cold one, never the other way. that's a irreversible process. Now suppose you want to change the temperature of a system through some reversible process. If you simply place the system in contact with an environment that is at a different temperature, as explained above heat will flow in a irreversible way. Instead you must place the system in contact with an environment that is at the same temperature as the system and than change the environments temperature very slowly (infinitesimally so). That way all parts of the system and environment are always at the same temperature (equilibrium) and any heat transferred between them can be reversed. That's of course an idealization that cannot be achieved in the real world because it requires an infinite amount of time.

1 person
Nikitin said:
Could you please explain it less formally, and more intuitively?Sent from my iPhone using Physics Forums
"Reversible" MEANS that the process can be reversed without materially changing any property of the system or surroundings.

I don't know how your intuition works. Perhaps you could explain what it is about this definition that you are having difficulty grasping.

Reversibility is a thermodynamic concept that can be approached but never actually achieved in practice.

AM

Ok, thanks dauto, I think I get it now. Thanks to AM, too.

Andrew Mason said:
"Reversible" MEANS that the process can be reversed without materially changing any property of the system or surroundings.

I don't know how your intuition works. Perhaps you could explain what it is about this definition that you are having difficulty grasping.

Reversibility is a thermodynamic concept that can be approached but never actually achieved in practice.

AM

I think I understood what Nikitin wanted to ask!

AM you said that there should be infinitesimally small difference in properties between the system and surroundings to reverse the process at any stage by introducing an infinitesimal change in conditions to reverse the direction of change.

This is the precise condition for a quasi equilibrium process where the process needs to be carried out extremely slowly so that effect of change is realized at all parts of the system and properties could be fixed for each equilibrium state.

For a reversible process the only fundamental requirement is that both the system and the surroundings be restored to their initial states after a reversal.

Andrew Mason said:
If the process involves heat transfer between the system and surroundings it has to be done with an infinitessimal temperature difference between the system and surroundings (so that an infinitessimal change in temperature willl cause the heat flow direction to reverse). This effectively means that the heat transfer will take an arbitrarily long time.

What is the difference if we make a heat transfer between the system and surroundings with a considerably large temperature difference?Why won't the system and surroundings be restored to their initial states?

While it's clear you must ensure an infinitesimal difference in conditions to establish a quasi equilibrium process could you explain as to why a reversible process must be a quasi equilibrium process?

Andrew Mason said:
"Reversible" MEANS that the process can be reversed without materially changing any property of the system or surroundings.

AM

Andrew Mason said:
If the process involves heat transfer between the system and surroundings it has to be done with an infinitessimal temperature difference between the system and surroundings (so that an infinitessimal change in temperature willl cause the heat flow direction to reverse). This effectively means that the heat transfer will take an arbitrarily long time.

If it is an adiabatic process, an arbitrarily small change in the pressure of the surroundings will result in a change in the direction of the process. This means that the net pressure on or by the surroundings (Psurr - Psys) has to be arbitrarily close to 0 so it will proceed at an infinitessimally slow pace.

AM

You are changing the properties of the system or surroundings to reverse the direction of process which contradicts your previous statement

Soumalya said:
You are changing the properties of the system or surroundings to reverse the direction of process which contradicts your previous statement
An infinitesimal change in conditions is arbitrarily close to no change in conditions. If there is no change in conditions but the process reverses direction, then it is a reversible process.

It is all conceptual and theoretical, of course. It is not possible in the real world to have an arbitrarily small change in conditions. Reversibility is a theoretical limit that cannot be achieved in practice.

AM

Soumalya said:
I think I understood what Nikitin wanted to ask!

For a reversible process the only fundamental requirement is that both the system and the surroundings be restored to their initial states after a reversal.
The question is: how? A Carnot engine will operate on its own and perform useful work but the reverse process requires work being done on the system. Where does that mechanical energy come from? It comes from the Carnot engine doing work which is stored as potential energy. If you can get back to the original initial state by operating the engine in reverse using ONLY the energy produced from the forward process, then the process is reversible.
What is the difference if we make a heat transfer between the system and surroundings with a considerably large temperature difference?Why won't the system and surroundings be restored to their initial states?
Because more work is needed to restore the system and surroundings to the initial state than was produced in the forward process.

While it's clear you must ensure an infinitesimal difference in conditions to establish a quasi equilibrium process could you explain as to why a reversible process must be a quasi equilibrium process?
Because if it is not in equilibrium more than an infinitesimal change is needed to reverse the direction of the process. If there is a finite positive temperature difference between the hot reservoir and the system (i.e Th - Tsystem > δ > 0) the heat flow from hot reservoir to system will not reverse direction with an arbitrarily small change in temperature.

AM

Andrew Mason said:
Because more work is needed to restore the system and surroundings to the initial state than was produced in the forward process.

AM

What if between two end states a non quasi static path is chosen as both the forward and reverse processes such that the Q=0 and W=0 for the overall cycle and the system and surroundings are both restored to their initial states?

Is it possible?If not why?

Andrew Mason said:
Because if it is not in equilibrium more than an infinitesimal change is needed to reverse the direction of the process. If there is a finite positive temperature difference between the hot reservoir and the system (i.e Th - Tsystem > δ > 0) the heat flow from hot reservoir to system will not reverse direction with an arbitrarily small change in temperature.

"An infinitesimal difference in properties of the system and surroundings should reverse the direction of process"

Is this the actual definition for a reversible process?Or it's a criterion to satisfy the actual definition for a reversible process?If it's an essential criterion for a reversible process could you illustrate by an example to show that an irreversible process is accompanied with more expenditure of energy for the reverse process?

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## 1. Why is it important for a process to be reversible in thermodynamics?

In thermodynamics, a reversible process refers to a process that can be reversed without causing any change to the system or its surroundings. This is important because it allows us to accurately measure and calculate the thermodynamic properties of a system. It also serves as an idealized model for understanding the behavior of real systems.

## 2. What is an example of a reversible process in thermodynamics?

An example of a reversible process is an ideal gas expanding or compressing slowly and without friction in a perfectly insulated container. This process can be reversed by compressing or expanding the gas back to its original state, without any loss of energy or change in the system's properties.

## 3. Can irreversible processes occur in thermodynamics?

Yes, irreversible processes can occur in thermodynamics. In fact, most real-life processes are irreversible. For example, the combustion of fuel in an engine, or the transfer of heat from a hot object to a colder one, are both irreversible processes.

## 4. How does the reversibility of a process affect the efficiency of a system?

The reversibility of a process is directly related to the efficiency of a system. A reversible process is considered to be the most efficient since it does not incur any energy losses. However, in real systems, there are always some irreversible processes that result in energy losses, making the system less efficient.

## 5. Are there any practical applications of reversible processes in thermodynamics?

Yes, reversible processes have several practical applications in thermodynamics. One example is the use of reversible heat engines in power plants, where the heat energy is converted into mechanical work with maximum efficiency. Another application is the reversible expansion and compression of gases in refrigeration and air conditioning systems, where the heat is either removed or added to the refrigerant to maintain a desired temperature.

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