Prove irreversibility in this quasi-static process.

[benny_91]

Consider a piston-cylinder arrangement with an ideal gas inside the cylinder. The region outside this arrangement or thermodynamic system is absolute vacuum. The piston has some mass and initially everything is in equilibrium. The inner surface of the cylinder is rough hence friction force comes into picture when there is relative motion between the piston and the cylinder. Now let the gas be compressed very slowly i.e the process is a quasi-static process (imagine infinitesimally small amount of weights being placed over the piston one by one). Now prove that is process irreversible using the most basic definition of irreversibility alone. Neglect radiation.
Definition: A process is said to be irreversible if it can be brought back to its original state without leaving any impact on the universe.

 

[Replusz]

I think your definition of irreversible is incorrect. You perfectly defined 'reversible'

 

[benny_91]

I think your definition of irreversible is incorrect. You perfectly defined 'reversible'

My bad! Please show me how this process leaves an impact on the universe when reversed!

 

[Andrew Mason]

My bad! Please show me how this process leaves an impact on the universe when

A process is reversible if the system and surroundings can be returned to their original states by an infinitessimal change in conditions. In this case you cannot return to the original state without adding energy from some outside source. You can't get the piston go expand to the original volume and return all the weights to their original locations without some additional energy. This is because the work done against friction cannot be fully converted into mechanical work.

AM

 

[benny_91]

A process is reversible if the system and surroundings can be returned to their original states by an infinitessimal change in conditions. In this case you cannot return to the original state without adding energy from some outside source. You can't get the piston go expand to the original volume and return all the weights to their original locations without some additional energy. This is because the work done against friction cannot be fully converted into mechanical work.

AM

But there will not be any energy loss from the system. All the heat energy released due to frictional effects will be well contained in the system raising the temperature of the gas. Now when the system is brought back to its original state the change in internal energy over the entire cycle will be zero. That means the extra energy which was released due too friction was later utilized during expansion and the temperature of the gas returns to its original value. Is this correct?

 

[Andrew Mason]

But there will not be any energy loss from the system. All the heat energy released due to frictional effects will be well contained in the system raising the temperature of the gas. Now when the system is brought back to its original state the change in internal energy over the entire cycle will be zero. That means the extra energy which was released due too friction was later utilized during expansion and the temperature of the gas returns to its original value. Is this correct?

There is no loss of energy to the system (first law). But there is gain in entropy and, therefore, a loss of the system's ability to do mechanical work (second law). The system will end up warmer than when it started and the piston will be lower than when it started. So it is not reversible.

 

[Chestermiller]

I think we need some equations to help us better analyze this problem. The first step should be to apply what we know to quantify the changes that occur in the irreversible compression. After that, we can focus on how we might try to return both the system and the surroundings to their original states, without causing significant changes in anything else. Andrew and Benny: what do you think of what I am proposing? If you both agree, I will try to propose a manageable path for the irreversible process, and we can analyze that.

Chet

 

[Andrew Mason]

I think we need some equations to help us better analyze this problem. The first step should be to apply what we know to quantify the changes that occur in the irreversible compression. After that, we can focus on how we might try to return both the system and the surroundings to their original states, without causing significant changes in anything else. Andrew and Benny: what do you think of what I am proposing? If you both agree, I will try to propose a manageable path for the irreversible process, and we can analyze that.

Chet

Hi Chet. I am not sure that it requires quantification but it should be easy to show that the change in entropy of the cylinder > 0. One just has to focus on the cylinder since the compression or expansion of the gas is adiabatic.

AM

 

[Chestermiller]

Hi Chet. I am not sure that it requires quantification but it should be easy to show that the change in entropy of the cylinder > 0. One just has to focus on the cylinder since the compression or expansion of the gas is adiabatic.

AM

That's what makes this problem so complicated and difficult. You are supposed to prove the contention without invoking entropy.

"Now prove that is process irreversible using the most basic definition of irreversibility alone.
Definition: A process is said to be irreversible if it can (not) be brought back to its original state without leaving any impact on the universe."

 

[benny_91]

I think we need some equations to help us better analyze this problem. The first step should be to apply what we know to quantify the changes that occur in the irreversible compression. After that, we can focus on how we might try to return both the system and the surroundings to their original states, without causing significant changes in anything else. Andrew and Benny: what do you think of what I am proposing? If you both agree, I will try to propose a manageable path for the irreversible process, and we can analyze that.

Chet

Hey Chet. I think quantifying will help us make precise conclusions. I shall try and come up with something!

 

[Andrew Mason]

That's what makes this problem so complicated and difficult. You are supposed to prove the contention without invoking entropy.

"Now prove that is process irreversible using the most basic definition of irreversibility alone.
Definition: A process is said to be irreversible if it can (not) be brought back to its original state without leaving any impact on the universe."

My use of entropy was in response to Benny's #5 post. The reason the process is not reversible is that the direction of the process cannot be changed with an infinitesimal change of conditions. Due to the friction, it takes a finite amount of pressure difference between the pressure on the cylinder and the pressure on the gas inside in order to compress the gas. So an infinitesimal change in pressure will not result in a reversal of direction (which requires a greater pressure in the gas than on the cylinder - and by an amount sufficient to overcome friction). You would have to remove more than an infinitesimal weight just to reverse the direction.

AM

 

[benny_91]

There is no loss of energy to the system (first law). But there is gain in entropy and, therefore, a loss of the system's ability to do mechanical work (second law). The system will end up warmer than when it started and the piston will be lower than when it started. So it is not reversible.

Hello I tried to solve this problem by forming equations and what I found out was similar to what you said. On trying to take back the system to its original state using a quasi static process one thing that was observed was that the system does not trace the original path. Apart from this when the system attains its original volume the pressure and temperature will not be the ones which we had started with in the beginning. The extra work which was done to overcome friction gets converted into heat energy which retains in the system increasing its pressure and temperature. So thank you!