The maxium possible efficiency of a heat engine is

Options

A. 1
B. `T_1/T_2`
C. `T_1/T_2+1`
D. Dependent upon the temperature of source `(T_1)`

Answer

To determine the maximum possible efficiency of a heat engine, we can use the principles of thermodynamics, specifically the Carnot efficiency. The Carnot efficiency is defined based on the temperatures of the heat source (T1) and the heat sink (T2).

### Step-by-Step Solution:

1. **Understanding Efficiency**:
The efficiency (η) of a heat engine is defined as the ratio of the work output (W) to the heat input (Q_in). Mathematically, it is expressed as:
\[ \eta = \frac{W}{Q_{in}} \]

2. **Carnot Efficiency Formula**:
The maximum possible efficiency of a heat engine operating between two thermal reservoirs is given by the Carnot efficiency formula:
\[ \eta_{max} = 1 - \frac{T_2}{T_1} \]
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).

3. **Rearranging the Formula**:
The formula can also be expressed in terms of temperatures:
\[ \eta_{max} = \frac{T_1 - T_2}{T_1} \]
This shows that the efficiency depends on the temperature difference between the source and the sink.

4. **Analyzing the Options**:
Given the options:
- Option 1: Efficiency = 1
- Option 2: Efficiency = \(\frac{T_1}{T_2}\)
- Option 3: Efficiency = \(\frac{T_1}{T_2} + 1\)
- Option 4: Efficiency depends on the temperature of the source.

We see that the maximum efficiency does not equal 1 (as that would imply 100% efficiency, which is impossible), and the other options do not correctly represent the Carnot efficiency.

5. **Conclusion**:
The correct answer is that the maximum possible efficiency of a heat engine depends on the temperatures of the source and sink, specifically on the temperature of the source. Therefore, the correct option is:
\[ \text{Final Answer: Option 4} \]