How does Carnot Cycle Expand and Compress Isentropically?

• I<3NickTesla
In summary, the Carnot cycle involves four stages where heat is transferred from a hot reservoir to a cold reservoir, with work being done on the surroundings during stages 1 and 2 and on the system during stages 3 and 4. The net effect is a conversion of heat into work, with the use of small weights to assist in the compression and expansion steps. The amount of work provided by the cycle depends on the difference in heat transfer between the two reservoirs.
I<3NickTesla

Homework Statement

I think I understand the first 3 steps of the Carnot cycle but not the 4th.

Homework Equations

The cycle here:
http://en.wikipedia.org/wiki/Carnot_cycle#Stages

The Attempt at a Solution

I understand that in stage 1, the gas expands by taking in heat from the hot reservoir and expanding to maintain constant temperature of the high temp reservoir.
Then in stage 2, the gas is allowed to do work on the surroundings by expanding more, this time cooling as it expands because it's not taking in any heat from the hot reservoir as it's adiabatic.
For stage 3, the cold reservoir takes away heat from the gas allowing it to compress it at constant temperature - the gas would cool if it was in contact with the cold reservoir at constant volume, but allowing it to compress keeps it at constant temperature.

Then in stage 4, the gas apparently compresses because the surroundings do work on it. But where is this work coming from? If the gas is at the cool temperature, it will be near enough at the same temperature as the surroundings so why would there be a pressure difference to allow it to compress?

I<3NickTesla said:

Homework Statement

I think I understand the first 3 steps of the Carnot cycle but not the 4th.

Homework Equations

The cycle here:
http://en.wikipedia.org/wiki/Carnot_cycle#Stages

The Attempt at a Solution

I understand that in stage 1, the gas expands by taking in heat from the hot reservoir and expanding to maintain constant temperature of the high temp reservoir.
Then in stage 2, the gas is allowed to do work on the surroundings by expanding more, this time cooling as it expands because it's not taking in any heat from the hot reservoir as it's adiabatic.
For stage 3, the cold reservoir takes away heat from the gas allowing it to compress it at constant temperature - the gas would cool if it was in contact with the cold reservoir at constant volume, but allowing it to compress keeps it at constant temperature.

Then in stage 4, the gas apparently compresses because the surroundings do work on it. But where is this work coming from?
We are part of the surroundings, and we can force the gas to compress (adiabatically) in stage 4. This can be done in a number of ways. One way is to gradually load a sequence of small weights onto the top of the piston. Another way is to gradually increase the force on the piston by hand, so that we personally are doing the work.
If the gas is at the cool temperature, it will be near enough at the same temperature as the surroundings so why would there be a pressure difference to allow it to compress?
Stage 4 is carried out adiabatically, and the temperature and pressure of the gas being compressed rises back up to the original temperature and pressure we started with at the beginning of stage 1. Then we can again carry out the isothermal expansion in stage 1 at the same temperature and pressure we did previously.

Chet

Chestermiller said:
We are part of the surroundings, and we can force the gas to compress (adiabatically) in stage 4. This can be done in a number of ways. One way is to gradually load a sequence of small weights onto the top of the piston. Another way is to gradually increase the force on the piston by hand, so that we personally are doing the work.

Stage 4 is carried out adiabatically, and the temperature and pressure of the gas being compressed rises back up to the original temperature and pressure we started with at the beginning of stage 1. Then we can again carry out the isothermal expansion in stage 1 at the same temperature and pressure we did previously.

Chet
Thanks for getting back so quickly.

I thought the point of a heat engine was to convert heat into work, so it seems weird if we have to do work on the system to make it function.

Is there some sort of feedback where the work done by the expansion is stored, then used to compress the gas again later?

Last edited:
I<3NickTesla said:
Thanks for getting back so quickly.

I thought the point of a heat engine was to convert heat into work, so it seems weird if we have to do work on the system to make it work.

Is there some sort of feedback where the work done by the expansion is stored, then used to compress the gas again later?
You are doing more work during the expansion steps (1 & 2) than you are expending during the compression steps (3 & 4). So the net effect is to absorb heat from the hot reservoir, transfer a smaller amount of heat to the cold reservoir, and use the difference to do a net amount of work. During the compression steps, you can be adding small weights to the top of the piston at various low elevations, and, during the expansion steps, you can be removing the weights from the piston at various higher elevations. The net effect of one cycle is that you have raised the entire series of weights to various higher elevations. Then you can repeat the process with a new set of weights.

Chet

Chestermiller said:
You are doing more work during the expansion steps (1 & 2) than you are expending during the compression steps (3 & 4). So the net effect is to absorb heat from the hot reservoir, transfer a smaller amount of heat to the cold reservoir, and use the difference to do a net amount of work. During the compression steps, you can be adding small weights to the top of the piston at various low elevations, and, during the expansion steps, you can be removing the weights from the piston at various higher elevations. The net effect of one cycle is that you have raised the entire series of weights to various higher elevations. Then you can repeat the process with a new set of weights.

Chet
So is the number given as the work provided by a Carnot engine the difference between the work done by the gas expanding and the work you have to do on the gas to compress it back to its original state?

I<3NickTesla said:
So is the number given as the work provided by a Carnot engine the difference between the work done by the gas expanding and the work you have to do on the gas to compress it back to its original state?
Yes.

1. What is the Carnot Cycle?

The Carnot Cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

2. How does the Carnot Cycle expand isentropically?

The isentropic expansion process in the Carnot Cycle is a reversible adiabatic process, meaning that no heat is transferred and the system remains in thermal equilibrium. This expansion is also isentropic, meaning that there is no change in entropy, and the gas expands in a way that maintains a constant entropy level.

3. How does the Carnot Cycle compress isentropically?

The isentropic compression process in the Carnot Cycle is also a reversible adiabatic process, where no heat is transferred and the system remains in thermal equilibrium. This compression is also isentropic, meaning that there is no change in entropy, and the gas is compressed in a way that maintains a constant entropy level.

4. What is the purpose of expanding and compressing isentropically in the Carnot Cycle?

Expanding and compressing isentropically in the Carnot Cycle is essential for maintaining the maximum efficiency of the cycle. These processes ensure that the system remains in thermal equilibrium and does not lose any energy to the surroundings, resulting in the most efficient conversion of heat into work.

5. How does the Carnot Cycle expand and compress isentropically compared to other thermodynamic cycles?

The Carnot Cycle is considered to be the most efficient thermodynamic cycle because of its isentropic expansion and compression processes. Other thermodynamic cycles, such as the Otto and Diesel cycles, involve non-isentropic processes, which result in lower efficiency. Therefore, the Carnot Cycle is used as the theoretical benchmark for the maximum efficiency of all other thermodynamic cycles.

Replies
2
Views
1K
Replies
3
Views
770
Replies
4
Views
2K
Replies
7
Views
2K
Replies
7
Views
2K
Replies
14
Views
8K
Replies
7
Views
3K
Replies
1
Views
1K
Replies
2
Views
2K
Replies
1
Views
1K