Clarifying the Cooling Stages of a Carnot Engine

[tiredryan]

Note this is more of a coursework question about the theory behind Carnot engines as opposed to an actual homework question.

Homework Statement

The Attempt at a Solution

So I am reading the theory behind a Carnot Engine and I am a little confused about the cooling stages of the Carnot cycle. This is steps 3 and 4 called, "Reversible isothermal compression of the gas at the "cold" temperature, TC" and "Isentropic compression of the gas(isentropic work input)" at http://en.wikipedia.org/wiki/Carnot_cycle#The_Carnot_cycle.

From my reading, it seems to be that some work has to be done on the system to return the piston to its lower volume stage. Basically part of the work that was created to push the piston out is used to return the piston back in. Is this a correct understanding?

If so, I am confused when thinking about the following thought experiment. Let's imagine that I had a balloon filled with gas connected to a shaft connected to an object I wanted to apply work on. When I place the balloon in a hot bath the balloon expands and the shaft moves and the object moves. The the shaft pushes the object over a distance and work is done on the object. When I switch out the balloon into cold water, the balloon shrinks and the object moves back. The object is moved by the force applied from the shaft and work is done on the object again. So in the forward cycle and the backward cycle work is being done to push the object. When I move the balloon cold water, I do not need to apply any addition work, but rather work is being done to the object of interest.

I am not sure where my confusion stems. Thanks in advance.

 

[vela]

From my reading, it seems to be that some work has to be done on the system to return the piston to its lower volume stage. Basically part of the work that was created to push the piston out is used to return the piston back in. Is this a correct understanding?

Essentially yes. Work has to be done to restore the system back to its initial state, but it doesn't necessarily have to be part of the work output from the earlier part of the process.

If so, I am confused when thinking about the following thought experiment. Let's imagine that I had a balloon filled with gas connected to a shaft connected to an object I wanted to apply work on. When I place the balloon in a hot bath the balloon expands and the shaft moves and the object moves. The shaft pushes the object over a distance and work is done on the object. When I switch out the balloon into cold water, the balloon shrinks and the object moves back. The object is moved by the force applied from the shaft and work is done on the object again. So in the forward cycle and the backward cycle work is being done to push the object. When I move the balloon cold water, I do not need to apply any addition work, but rather work is being done to the object of interest.

I am not sure where my confusion stems. Thanks in advance.

It's implied in your description that the object comes to rest in between the two phases. As it decelerates, it's doing work on the gas. Also, when the gas cool, it will contract only if something outside does work. In this case, both the balloon and the outside atmosphere will perform work, and part of the work goes into accelerating the object.

 

[kerimek]

I can provide some clarification on the Carnot engine theory and address your confusion about the cooling stages.

Firstly, it is important to understand that a Carnot engine is a theoretical model and does not necessarily represent a real-life engine. It is used as a benchmark for comparing the efficiency of real engines. In a Carnot engine, the cooling stages involve the gas being compressed isothermally (at a constant temperature) and isentropically (without any heat transfer). This is done in order to maintain the temperature difference between the hot and cold reservoirs, which is necessary for the engine to operate.

To address your specific question about the work done in the cooling stages, it is correct that some work is required to return the piston to its lower volume stage. This work is done by the engine itself, as it is being driven by the heat transfer from the hot reservoir. This work is necessary to maintain the temperature difference and to keep the engine running. In the thought experiment you described, the work being done on the object is actually being done by the engine, and not by the balloon itself.

It is also important to note that in the Carnot cycle, the efficiency of the engine is determined by the temperature difference between the hot and cold reservoirs, and not by the specific work done in the cooling stages. This means that the work done in the cooling stages may not necessarily be equal to the work done in the heating stages, as long as the temperature difference is maintained.

I hope this helps to clarify your understanding of the Carnot engine theory. If you have any further questions, please don't hesitate to ask.