Understanding a proof of Carnot's theorem.

[Fallen Seraph]

[SOLVED] Understanding a proof of Carnot's theorem.

I'm having trouble understand this proof of Carnot's theorem, and I would appreciate it if someone could point out where my reasoning goes wrong.

The proof reads thusly:

Suppose there exists a a hypothetical engine with a greater efficiency than a Carnot engine.

Consider this engine working from the same hot and cold reservoirs as a Carnot engine.

Adjust the cycle of the Carnot engine such that its work output == that of the hypothetical engine == W

Since the Carnot engine is reversable, we can turn it into a refrigerator that takes in work W from the hypothetical engine and energy Q2 from the cold reservoir and then outputs energy Q1 into the hot reservoir.

Let the energy taken from the hot reservoir by the hypothetical engine == P1.

We have that the efficiency of the hypothetical engine is greater than that of the Carnot one, so

W/P1>W/Q1

=>

Q1>P1.

This means that our construction is taking heat from the cold reservoir, and depositing it in the hot one. Which violates the 2nd law, and thus proves the theorem.

My problem with it is that is seems to imply that either the second law is wrong, or the Carnot engine is not the most efficient because:

Why not just get an engine that is less efficient than the Carnot one and construct the same device as was made in the proof except with the Carnot engine in the place that the hypothetical one occupied in the proof, and the less efficient engine in the place of the Carnot?

This, as far as I can see, would also move heat from the cold reservoir to the hot one.

What am I missing?

Thanks in advance.

 

[Cthugha]

What am I missing?

Any process with efficiency less than Carnot efficiency is not reversible, for example.

 

[Fallen Seraph]

Ah! So it is!

Thank you.

 

[nikolafmf]

This Carnot engine works as refrigerator. So, shouldn't it eficiency be Q₂/W and not W/Q₁?

 

[Swarnali Hait]

that's not efficiency,that's co-efficient of performance..
we are working with efficiency here so if we take coefficient of performance we must have to convert it into efficiency through the relation between them finally..:)