Carnot Cycle and Line Integrals

[longbusy]

I have to corellate the Carnot cycle with line integrals. This makes sense to me as line integrals can be used to find the work done by a vector field on an object traveling along a certain path. The Carnot cycle places a limit on the efficiency of an engine cycle.

My question, how could I specifically compare line integrals to the Carnot cycle. Maybe the effect that heat has on the system? I'll attach what I have written so far. Thanks!

(Edit: I attached the .doc file but I do not see it on my post.)

 

[climbhi]

You could try using Green's theorem to relate the Line Integrals around the cycle to the area inside the region, however since when using Green's theorem you usually go around the region counterclockwise it would be in the wrong direction of your cylce.

 

[dg]

Originally posted by longbusy
I have to corellate the Carnot cycle with line integrals. This makes sense to me as line integrals can be used to find the work done by a vector field on an object traveling along a certain path. The Carnot cycle places a limit on the efficiency of an engine cycle.

My question, how could I specifically compare line integrals to the Carnot cycle. Maybe the effect that heat has on the system? I'll attach what I have written so far. Thanks!

You might want to start having a look at http://scienceworld.wolfram.com/physics/topics/ThermodynamicCycles.html.
The first remark on your doc is that you are assuming car engines run on a Carnot Cycle which is not true since gasoline cars use Otto cycle and diesel cars use Diesel cycle.

Besides that you have to consider that Carnot Cycle is an ideal representation valid for quasi-static (reversible) transformations. This ideal representation set a limit to real world engines through the so called Clausius Theorem that is based on line integrals.

I will write you more tomorrow... search the internet for a decent thermodynamic textbook.

DArio