# Is Carnot engine the only reversible engine?

Gold Member
Is Carnot engine the only form of reversible engine? Is it possible to have a different form of reversible engine that goes through different processes?

For a standard Otto cycle working with ideal gas, theoretically the two processes involving isochoric pressure change can be reversible processes. Does it mean that the Otto cycle can also have same efficiency as Carnot cycle? Since temperature of the working fluid is changing during isochoric pressure change, does it mean there are infinite number of heat reservoirs being used at different temperatures so that there is no finite temperature difference at every point of the isochoric process?

The second law of thermodynamics states that the entropy of the universe continuously goes on increasing. Even though the system may arrive at the same state after every cycle, the heat dissipated to the surroundings during the isochoric expansion increases the entropy of the surroundings. For the Otto cycle to be reversible, it would have to violate the second law.

Gold Member
The second law of thermodynamics states that the entropy of the universe continuously goes on increasing. Even though the system may arrive at the same state after every cycle, the heat dissipated to the surroundings during the isochoric expansion increases the entropy of the surroundings. For the Otto cycle to be reversible, it would have to violate the second law.

What if we keep on replacing different temperature reservoir from time to time? If Otto cycle is irreversible, we cannot even draw it on the P-V diagram because the isochoric pressure increase/decrease are not quasi-equilibrium process.

Why not? Sure we can draw it on a P-V diagram. An irreversible process is just one which permantly changes surroundings. You cannot come back to the stage that was prevalent before the cycle took place.

Chestermiller
Mentor
Is Carnot engine the only form of reversible engine? Is it possible to have a different form of reversible engine that goes through different processes?

For a standard Otto cycle working with ideal gas, theoretically the two processes involving isochoric pressure change can be reversible processes. Does it mean that the Otto cycle can also have same efficiency as Carnot cycle? Since temperature of the working fluid is changing during isochoric pressure change, does it mean there are infinite number of heat reservoirs being used at different temperatures so that there is no finite temperature difference at every point of the isochoric process?
The answer to all your questions is YES. You have analyzed the situation flawlessly. Very nicely done. Of course, the combined change in entropy of the two sets of reservoirs will turn out to be zero.

Chet

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• kelvin490
Gold Member
The answer to all your questions is YES. You have analyzed the situation flawlessly. Very nicely done. Of course, the combined change in entropy of the two sets of reservoirs will turn out to be zero.

Chet

Thank you. I have one further question. How to compare the efficiency between a Carnot engine and an ideal Otto engine? As mentioned before in an ideal Otto engine there are infinite number of heat reservoirs being used at different temperatures so that there is no finite temperature difference at every point of the isochoric process. Carnot cycle involves only two reservoirs so it's easy to calculate the efficiency. For an ideal Otto cycle many reservoirs involved so I wonder what's the basis of comparison?

Chestermiller
Mentor
Thank you. I have one further question. How to compare the efficiency between a Carnot engine and an ideal Otto engine? As mentioned before in an ideal Otto engine there are infinite number of heat reservoirs being used at different temperatures so that there is no finite temperature difference at every point of the isochoric process. Carnot cycle involves only two reservoirs so it's easy to calculate the efficiency. For an ideal Otto cycle many reservoirs involved so I wonder what's the basis of comparison?
Excellent questions. For the Otto cycle, you can of course model it yourself to derive an equation for the efficiency, or you can check out this link: http://en.wikipedia.org/wiki/Otto_cycle. In this link, they do the analysis for you. If it were me and I really wanted to get some practice, I would model it myself; otherwise, I would just see what they do in the link.

Chet

• kelvin490
Thank you. I have one further question. How to compare the efficiency between a Carnot engine and an ideal Otto engine? As mentioned before in an ideal Otto engine there are infinite number of heat reservoirs being used at different temperatures so that there is no finite temperature difference at every point of the isochoric process. Carnot cycle involves only two reservoirs so it's easy to calculate the efficiency. For an ideal Otto cycle many reservoirs involved so I wonder what's the basis of comparison?

For calculating the efficiency of an Otto cycle, use the basic principle of efficiency. How much was the heat input, how much of it was converted to work and how much heat was wasted. You can get an equation in the form of 'T'.

• kelvin490
Gold Member
For calculating the efficiency of an Otto cycle, use the basic principle of efficiency. How much was the heat input, how much of it was converted to work and how much heat was wasted. You can get an equation in the form of 'T'.

Agree. But I think we can only get the equation in terms of ratio of T instead of the exact temperature, since there are numbers of reservoirs and we don't have the criteria for selecting one of them as a representative heat reservoir. Is that correct?

Chestermiller
Mentor
Agree. But I think we can only get the equation in terms of ratio of T instead of the exact temperature, since there are numbers of reservoirs and we don't have the criteria for selecting one of them as a representative heat reservoir. Is that correct?
What do they end up with in the Wiki article?

• kelvin490
Agree. But I think we can only get the equation in terms of ratio of T instead of the exact temperature, since there are numbers of reservoirs and we don't have the criteria for selecting one of them as a representative heat reservoir. Is that correct?

You're right. You get it as a ratio of temperatures. But The ratio is of temperatures at the start and end of a process. The infinite number of temperature reservoirs is a concept used to explain the process. Don't be stuck on that.

• kelvin490
Gold Member
What do they end up with in the Wiki article?

Oh, yes. They express it in terms of changes in internal energy first and express in terms of initial and final temperatures. Thanks a lot.