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 moles

Answer

To determine which statement is incorrect regarding the efficiency of reversible cycles, let's analyze the options provided step by step.

### Step 1: Understanding Reversible Cycles
Reversible cycles are idealized thermodynamic processes where the system can be returned to its initial state without any net change in the surroundings. The most well-known reversible cycle is the Carnot cycle, which operates between two thermal reservoirs.

### Step 2: Efficiency of Reversible Cycles
The efficiency of a Carnot cycle (reversible cycle) is given by the formula:
\[ \eta = 1 - \frac{T_L}{T_H} \]
where \( T_L \) is the absolute temperature of the cold reservoir and \( T_H \) is the absolute temperature of the hot reservoir. This indicates that the efficiency depends on the temperatures of the reservoirs.

### Step 3: Analyzing the Statements
- **Option A**: "All reversible cycles have the same efficiency."
- This statement is incorrect because the efficiency of reversible cycles varies depending on the temperatures of the hot and cold reservoirs. Therefore, not all reversible cycles have the same efficiency.

- **Option B**: "Reversible cycle has more efficiency than irreversible."
- This statement is correct. Reversible cycles, by definition, have maximum efficiency compared to irreversible cycles, which always have lower efficiency due to irreversibilities and losses.

### Conclusion
From the analysis, we conclude that **Option A** is the incorrect statement.