# Queries about the carnot cycle

So I was studying the carnot cycle and was taught it as the following sequence.

Imagine a cylinder filled with some ideal gas at $$T_1$$. It has some rocks on top of it and the system is in equilibrium. If you place it in a reservoir at temperature $$T_1$$, and remove the small rocks one by one, you can treat this as an isothermal expansion.

Then follows an adiabatic expansion, by removing more small rocks while keeping the system thermally isolated.

After which point the system will reach a lower temperature $$T_2$$. Placing it again in a reservoir at $$T_2$$ and adding rocks back will compress the gas isothermally.

The final part is an adiabatic compression back to the initial point in the phase diagram, done by adding more rocks while the system is kept in thermal isolation.

This is my understanding of a carnot cycle.

My question is that, how is this system doing any work? I understand how to calculate the work done on a phase diagram. The main concern is that isnt the work done by us in removing and adding the rocks balanced by the work done by the piston in moving up and down? Isn't the overall work done still 0?

Secondly what is the significance of the isothermal adiabatic expansion / contraction sequence. My previous impression was that any loop in a phase diagram was reversible if the process was done slowly. Is the efficiency of reversible processes not the same? What is it about the carnot cycles sequence that gives it the greatest efficiency?

Not sure if these questions are coherent but I am still not clear on why the carnot engine seems to be such a big deal.

The main concern is that isnt the work done by us in removing and adding the rocks balanced by the work done by the piston in moving up and down?

Each rock is slid off the piston horizontally during the isothermal and adiabatic expansions, and slid back onto the piston horizontally, during the isothermal and adiabatic compressions. No work is associated with the horizontal movement of the rocks against or with gravity. Work is done by the gas on the remaining rocks by raising them against gravity during the expansions, and work is done by the rocks on the gas during the compressions when the remaining rocks are lowered.

This example of the rocks is one of many ways to visualize how to meet the requirement that the cycle be carried out extremely (infinitely) slowly so that the system is always in thermal and mechanical equilibrium with its surroundings. In fact, the usual example is removal of grains of sand, one grain at a time. The Carnot cycle is an idealization to establish the maximum theoretical efficiency of any heat engine operating in a cycle. It is never practically used because it proceeds infinitely slowly. As someone once said, if you put a Carnot engine in your car you would get fantastic fuel economy, but pedestrians would be passing you by!

Isn't the overall work done still 0?

Given the explanation of the rocks, and the fact that you said you know how to calculate the work from the diagram, you should see that net work is done in the cycle. The net work done is really the difference between the magnitude of the work done by the gas during the isothermal expansion, minus the magnitude of the work done on the gas during the isothermal compression. The two adiabatic works cancel out.

Secondly what is the significance of the isothermal adiabatic expansion / contraction sequence.

The reversible isothermal expansion is how the system does work on the surroundings by taking in heat isothermally from the surroundings. The isothermal compression allows the system to reject the heat that is always necessary due to the second law.

The reversible adiabatic processes allow the cycle to be completed without needing any heat exchange and change in entropy. The adiabatic expansion brings the system to the lower temperature reservoir $$T_2$$ for the isothermal compression to take place. At the end of the isothermal compression the internal energy of the gas is still lower than the starting internal energy. Since all properties, including internal energy, must return to their original values at the completion of the cycle, the adiabatic compression is needed to increase the internal energy back to its original state, without causing any entropy change, since entropy too must return to its original state.

My previous impression was that any loop in a phase diagram was reversible if the process was done slowly.

Yes, provided that in addition there is no friction involved because a process can be carried out slowly and still involve friction.

Is the efficiency of reversible processes not the same? What is it about the carnot cycles sequence that gives it the greatest efficiency

One of the main things that differentiates the Carnot cycle from other reversible cycles is the isothermal expansion and compression. In contrast to any other reversible processes that take in and reject heat, all the heat into the system occurs at the same high temperature, $$T_1$$, and all of the heat out at the same low temperature, $$T_2$$. For other processes the heat exchanges occur at some mean (average) temperature. This maximizes the efficiency of the Carnot cycle by minimizing $$\frac{T_2}{T_1}$$ in the equation for efficiency $$1-\frac{T_2}{T_1}$$. This is best visualized by looking at the temperature-entropy diagram.

Hope this helps.

My understanding is Carnot Cycle is an ideal cycle that cannot be achieved its purpose is to find the limit of efficiency of heat engine or refrigerator, it matters little of how much work can be done.
Carnot engines have greatest efficiency because Carnot cycle is "perfectly reversible" and if you combine both reversed and non-reversed cycles you get a system that transfers heat from cold reservoir to hot reservoir without any help, this is against the second law of thermodynamics.