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 follow these steps:

### Step 1: Understand the concept of efficiency
The efficiency (η) of a heat engine is defined as the ratio of the work output (W) to the heat input (Q_H) from the heat source. Mathematically, it can be expressed as:
\[ η = \frac{W}{Q_H} \]

### Step 2: Apply the Carnot efficiency formula
The maximum possible efficiency of a heat engine operating between two temperatures is given by the Carnot efficiency formula:
\[ η_{max} = 1 - \frac{T_C}{T_H} \]
where:
- \(T_H\) is the absolute temperature of the heat source (in Kelvin),
- \(T_C\) is the absolute temperature of the cold sink (in Kelvin).

### Step 3: Rearrange the formula
We can rearrange the Carnot efficiency formula to express it in terms of the temperatures:
\[ η_{max} = \frac{T_H - T_C}{T_H} \]
This shows that the efficiency depends on the temperatures of the heat source and sink.

### Step 4: Analyze the options
Now, let's analyze the given options:
1. Option 1: 1
2. Option 2: \( \frac{T_1}{T_2} \)
3. Option 3: \( \frac{T_1}{T_2} + 1 \)
4. Option 4: Dependent upon the temperature of the source \(T_1\)

From the Carnot efficiency formula, we can see that the efficiency is indeed dependent on the temperature of the source \(T_H\) (or \(T_1\) in this context).

### Step 5: Conclusion
Thus, the maximum possible efficiency of a heat engine is dependent upon the temperature of the source. Therefore, the correct answer is:
\[ \text{Option 4: Dependent upon the temperature of the source } T_1 \]

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