# Quasi-equilibrium process

#### AAMAIK

I am self studying thermodynamics and I stumbled upon the concept of a quasi-equilibrium process which I dont fully understand but here are my thoughts, Equilibrium is a condition of balance characterized by the absence of driving potentials and at such conditions you can measure properties that describe the state of a system and that these properties are the same at every point in a system. This can be validated if our measurements don't diverge, if they were then we not at equilibrium. If a system undergoes a certain process, we are not in equilibrium, so how can we trace the path from one state to another ( namely the properties that describe the system are changing with time how can they be quantified) . In order for us to take measurements the system has to be in equilibrium, but again if we leave the system to come to equilibrium how can we be sure that the properties that describe the system in equilibrium are the same as those that described it at the point we decided to stop the process? To illustrate what I am trying to say in the last two sentences suppose I have a cup of water and I am heating it and I place a thermometer inside the cup of water to measure its temperature, the reading would be misleading, the water temperature close to the heat source would be higher than at the top and If I stop heating to allow the cup of water to reach equilibrium and again take a measurement of the temperature that reading would be different than my previous reading I allowed my cup of water to exchange heat with the surrounding. If we allow for an infinitesimal change in the set of properties that describe the current state of our system, we are guaranteed a process but why is this process slow, and how if we lump those assumptions allow us to take measurements that are representative of the system?

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#### mjc123

Suppose you have a system at equilibrium, and you make a small step change in the conditions (e.g. pressure or temperature - or perhaps one might say, position of a piston or injection of an amount of heat). Now you let the system re-establish equilibrium at the new conditions, then you make another step change and allow to re-equilibrate. And repeat and repeat.

Now make the steps - and the time interval between them - smaller. (The important thing is to allow the time interval to be long enough for the system to reach equilibrium at the new condition. Or put alternatively, for the response of the system to be fast enough to re-establish equilibrium within the time interval.) In the limit of infinitesimally small steps and intervals, you have a smooth process in which the system is effectively at equilibrium at every point. With very small but finite steps, you approximate to this.

To take the example of heating a cup of water, if the water was rapidly stirred, the added heat would be more quickly dissipated throughout the volume and you would have something much closer to a meaningful "temperature of the water" (not just of part of it), and if you stopped the heating you could measure an equilibrium temperature much faster and lose much less heat to the surroundings. And the smaller the temperature interval between stopping to make measurements, the faster the measurement would be.

#### AAMAIK

Suppose you have a system at equilibrium, and you make a small step change in the conditions (e.g. pressure or temperature - or perhaps one might say, position of a piston or injection of an amount of heat). Now you let the system re-establish equilibrium at the new conditions, then you make another step change and allow to re-equilibrate. And repeat and repeat.
I have a question regarding this point, in injecting an amount of heat for a certain duration, I want to measure the temperature (response of the system) to the heat added, in doing so should the system be an isolated system to ensure that the measurement is accurate in other words no external agent have altered the system properties?

Now make the steps - and the time interval between them - smaller. (The important thing is to allow the time interval to be long enough for the system to reach equilibrium at the new condition. Or put alternatively, for the response of the system to be fast enough to re-establish equilibrium within the time interval.) In the limit of infinitesimally small steps and intervals, you have a smooth process in which the system is effectively at equilibrium at every point. With very small but finite steps, you approximate to this.
A system takes a finite amount of time to establish equilibrium at the new condition, so in order to achieve a continuous process, a continuous path, this implies that the response of the system has to be fast enough( I don't want to say infinite, because its vague) and that introducing infinitesimally small steps to be at equilibrium at every point and most importantly fast enough?

#### Chestermiller

Mentor
I disagree with the requirement that the time intervals become smaller and smaller. Instead, the time intervals between changes must all be long enough for the system to essentially re-equilibrate. However, the changes at the boundary must become smaller and smaller so that, in the limit, we have a very slow continuous process. This is what I regard as a quasi-static process. If this is done, the system is never more than being only slightly removed from thermodynamic equilibrium with its surroundings at each instant.

#### AAMAIK

I still don't get why its a 'very slow' process, is this something we concluded from experiment?

#### Chestermiller

Mentor
I still don't get why its a 'very slow' process, is this something we concluded from experiment?
If the process is not very slow, there will be significant viscous dissipation of mechanical energy by finite velocity gradients and significant dissipation of thermal driving forces by finite conductive temperature gradients, both of which render the process irreversible.

#### AAMAIK

If the process is not very slow, there will be significant viscous dissipation of mechanical energy by finite velocity gradients and significant dissipation of thermal driving forces by finite conductive temperature gradients, both of which render the process irreversible.
I have not gone through irreversible/reversible processes's yet, I understand why we cannot depict a process path if were to conduct it in a fast manner. For example, Suppose we have a gaseous mixture in a cylinder and if we push down quickly on the piston, near the top of the piston gaseous molecules will be at a higher pressure than at the bottom. Any measurement of pressure to describe the state in such a scenario would be misleading. But I don't understand how if I applied my force slowly or quickly regardless of the pace, would this neglect the friction losses between the piston and the inner lining of the cylinder in which the gas is contained.

#### Chestermiller

Mentor
I have not gone through irreversible/reversible processes's yet, I understand why we cannot depict a process path if were to conduct it in a fast manner. For example, Suppose we have a gaseous mixture in a cylinder and if we push down quickly on the piston, near the top of the piston gaseous molecules will be at a higher pressure than at the bottom. Any measurement of pressure to describe the state in such a scenario would be misleading. But I don't understand how if I applied my force slowly or quickly regardless of the pace, would this neglect the friction losses between the piston and the inner lining of the cylinder in which the gas is contained.
What is happening to the gas inside the cylinder is somewhat more complicated than how you describe it. In a rapidly deforming gas, there are both pressure- and viscous contributions to the forces within the gas. The higher momentum of the molecules near the piston is transferred to the molecules further below by molecular collisions, which translate on the larger scale into viscous stresses. These are over and above the pressure stresses caused by local specific volume changes. The viscous stresses are dissipative in nature, fully analogous to friction from the piston. In addition to all that, since the gas has mass (inertia), rapid application of the piston, this causes variations in pressure due to compression waves traveling along the cylinder (like sound waves), and reflecting off the far wall.

But, by far, the more dominant dissipative effect is the viscous stresses. The viscous stresses are determined, not by the amount of volume change, but rather by the rate at which the volume is changing. Thus, not only is the displacement of the piston important, but also the velocity of the piston. In a very slow deformation, the rate of volume change is negligible, and so also are the viscous stresses; so the rate of mechanical energy dissipation becomes negligible in a very slow application of the piston.

Now let's talk about piston friction. If the piston is not frictionless, then it doesn't matter how fast the piston is moving. This results in dissipation of mechanical energy irrespective of the speed of the piston.

"Quasi-equilibrium process"

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