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

Options

A. 0
B. 1
C. 0.5
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-by-Step Solution:

1. **Understanding the Carnot Engine**:
The Carnot engine operates between two heat reservoirs: a hot reservoir at temperature \( T_1 \) and a cold reservoir (sink) at temperature \( T_2 \). 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 and \( T_2 \) is the absolute temperature of the cold reservoir.

2. **Identifying the Temperature of the Sink**:
In this case, the problem states that the temperature of the sink is at absolute zero, which is \( T_2 = 0 \, \text{K} \).

3. **Substituting the Values into the Efficiency Formula**:
Now, substituting \( T_2 = 0 \, \text{K} \) into the efficiency formula:
\[ \eta = 1 - \frac{0}{T_1} \]
This simplifies to:
\[ \eta = 1 - 0 = 1 \]

4. **Converting Efficiency to Percentage**:
The efficiency of the Carnot engine can also be expressed as a percentage. Since \( \eta = 1 \), this means:
\[ \eta = 100\% \]

5. **Conclusion**:
Therefore, if the temperature of the sink is at absolute zero, the efficiency of the Carnot engine will be 100%.

### Final Answer:
The efficiency of the Carnot engine when the temperature of the sink is at absolute zero is **100%**.