Two carnot engines A and B are operating between the same sink and source .Engine A uses an ideal gas as the working fluid ,while engine B uses van der waals gas as the working fluid .which one of the following is correct?

Options

A. The efficiency of engine A is less than that of engine B
B. The efficiency of engine A is equal to that of engine B
C. The efficiency of engine A is more than that of engine B
D. No comparision can be made

Answer

To solve the question regarding the two Carnot engines A and B, we can follow these steps:

### Step 1: Understand the Carnot Engine
A Carnot engine is an idealized heat engine that operates between two heat reservoirs: a hot reservoir (source) at temperature \( T_1 \) and a cold reservoir (sink) at temperature \( T_2 \). The efficiency of a Carnot engine is determined solely by these temperatures.

### Step 2: Write the Efficiency Formula
The efficiency \( \eta \) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_2}{T_1} \]
where:
- \( T_1 \) is the absolute temperature of the hot reservoir (source).
- \( T_2 \) is the absolute temperature of the cold reservoir (sink).

### Step 3: Analyze the Working Fluids
In this scenario:
- Engine A uses an ideal gas as the working fluid.
- Engine B uses a Van der Waals gas as the working fluid.

### Step 4: Determine the Effect of Working Substance on Efficiency
The key point to note is that the efficiency of a Carnot engine depends only on the temperatures \( T_1 \) and \( T_2 \) and not on the type of working substance used. This means that regardless of whether the working fluid is an ideal gas or a Van der Waals gas, the efficiency will remain the same as long as the engines operate between the same temperatures.

### Step 5: Conclusion
Since both engines A and B are operating between the same sink and source, their efficiencies will be equal. Therefore, the correct conclusion is that the efficiency of both engines is the same.

### Final Answer
The correct option is that the efficiencies of both engines A and B are the same.

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