If the temperature of sink is at absolute zero, then the efficiency of carnot engine will be

Options

A. 0
B. 1
C. `-50`%
D. 0.75

Answer

To determine the efficiency of a Carnot engine when the temperature of the sink is at absolute zero, we can follow these steps:

### Step 1: Understand the Carnot Engine Efficiency Formula
The efficiency (η) of a Carnot engine is given by the formula:
\[ η = 1 - \frac{T_2}{T_1} \]
where:
- \( T_1 \) is the absolute temperature of the heat source (in Kelvin).
- \( T_2 \) is the absolute temperature of the heat sink (in Kelvin).

### Step 2: Identify the Given Conditions
According to the question, the temperature of the sink \( T_2 \) is at absolute zero. Therefore:
\[ T_2 = 0 \, \text{K} \]

### Step 3: Substitute the Values into the Efficiency Formula
Now we can substitute \( T_2 \) into the efficiency formula:
\[ η = 1 - \frac{0}{T_1} \]

### Step 4: Simplify the Expression
Since \( \frac{0}{T_1} = 0 \), the equation simplifies to:
\[ η = 1 - 0 \]
Thus,
\[ η = 1 \]

### Step 5: Conclusion
The efficiency of the Carnot engine when the temperature of the sink is at absolute zero is:
\[ η = 1 \]

This means that the Carnot engine would be perfectly efficient under these conditions.