Which statement is incorrect?
(a) All reversible cycles have same efficiency
(b) Reversible cycle ha

Q: Why is the Carnot cycle considered to have maximum efficiency?

Because it consists entirely of reversible processes, eliminating any energy loss due to friction or heat dissipation, making it the theoretical upper limit for efficiency between two temperatures.

Q: Can two different reversible engines have the same efficiency?

Yes, but only if they operate between the exact same source and sink temperatures. If the temperatures are different, their efficiencies will be different.

Q: Is a Carnot cycle practically possible?

No, it is a theoretical idealization. Real-world processes always involve some irreversibility like friction or heat loss.

Q: Does the working substance affect the efficiency of a Carnot engine?

No, Carnot's theorem explicitly states that the efficiency of a reversible engine is independent of the nature of the working substance.

Question

Which statement is incorrect?

Options:

(A) All reversible cycles have same efficiency

(B) Reversible cycle has more efficiency than an irreversible one

(C) Carnot cycle is a reversible one

(D) Carnot cycle has the maximum efficiency in all cycles

Sigma Percentile · Accepted Answer

### The Quest for the Perfect Engine

When we study thermodynamics, one of the most fascinating concepts is the heat engine—a device that converts heat into work. But a fundamental question arises: Can we build a perfect engine? The answer lies in the Second Law of Thermodynamics and the brilliant insights of Nicolas Léonard Sadi Carnot.

In this problem, we are asked to identify the incorrect statement among four options related to reversible cycles and Carnot engines. Let's break down the physics behind each statement to find the culprit.

### The Efficiency of Reversible Cycles

Let's look at the first statement: "All reversible cycles have the same efficiency." Is this true?

To answer this, we need to recall the formula for the efficiency of a reversible Carnot engine:
$$ \eta = 1 - \frac{T_2}{T_1} $$
where $T_1$ is the absolute temperature of the hot reservoir (source) and $T_2$ is the absolute temperature of the cold reservoir (sink).

This elegant equation tells us a profound truth: the efficiency of a reversible engine depends **exclusively** on the temperatures of the source and the sink. It does not depend on the working substance or the specific design of the engine.

Therefore, if we have two different reversible engines operating between *different* pairs of temperatures, their efficiencies will be different. They will only have the same efficiency if they operate between the *exact same* source and sink temperatures. Thus, the blanket statement that "All reversible cycles have the same efficiency" is fundamentally **incorrect**.

### Carnot's Theorem and Maximum Efficiency

Now, let's validate the other statements to be absolutely sure. Carnot's theorem consists of two main parts:
1. No engine operating between two given heat reservoirs can be more efficient than a reversible engine operating between those same two reservoirs.
2. All reversible engines operating between the same two reservoirs have the same efficiency.

This immediately proves that a reversible cycle has more efficiency than an irreversible one operating between the same temperatures. Irreversible engines suffer from energy losses due to friction, turbulence, and heat dissipation, which inherently lowers their efficiency.

Furthermore, the Carnot cycle is the theoretical benchmark—it is a perfectly reversible cycle. Because it is reversible, it boasts the maximum possible efficiency for any engine operating between a given $T_1$ and $T_2$.

In conclusion, statements (b), (c), and (d) are perfectly aligned with the laws of thermodynamics. Statement (a) is the odd one out, making it the correct answer to our question!

Animated Solution for Physics - Thermodynamics: Which statement is incorrect?

Select Answer:

Visualized Solution

$Efficiency of Reversible Cycles$

$Carnot’s Theorem$

The Sigma Insight: Heat Engines and Refrigerators

The Quest for the Perfect Engine

The Efficiency of Reversible Cycles

Carnot's Theorem and Maximum Efficiency

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