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

Explanation

To determine which statement is incorrect regarding the efficiency of cycles in thermodynamics, we will analyze the statements one by one.

### Step-by-Step Solution:

1. **Understanding Reversible Cycles:**
- Reversible cycles operate between two temperature reservoirs. The efficiency of a reversible cycle depends on the temperatures of these reservoirs.

2. **Efficiency Formula:**
- The efficiency (η) of a reversible cycle can be expressed as:
\[ \eta = 1 - \frac{T_2}{T_1} \]
- Here, \(T_1\) is the temperature of the hot reservoir and \(T_2\) is the temperature of the cold reservoir.

3. **Different Temperatures for Different Cycles:**
- Since \(T_1\) and \(T_2\) can vary for different reversible cycles, the efficiency will also vary. Therefore, it is incorrect to state that all reversible cycles have the same efficiency.

4. **Analyzing the Statements:**
- **Statement 1:** "All reversible cycles have the same efficiency."
- This statement is **incorrect** because the efficiency depends on the specific temperatures of the reservoirs used in each cycle.
- **Statement 2:** "The efficiency of irreversible cycles is less than that of reversible cycles."
- This statement is **correct** as irreversible processes always have lower efficiency compared to reversible processes.
- **Statement 3:** "The Carnot cycle is a reversible cycle and has maximum efficiency."
- This statement is **correct**; the Carnot cycle is indeed a reversible cycle and it achieves maximum efficiency among all thermal cycles.

5. **Conclusion:**
- The first statement is the only incorrect statement among the options provided.

### Final Answer:
The incorrect statement is: "All reversible cycles have the same efficiency."

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