The value of `eta` may lie between

Options

A. 0 to 1
B. 1 to `oo`
C. `-1` to +1
D. 0 to `oo`

Answer

To solve the question regarding the possible values of efficiency (η) of a heat engine, we can follow these steps:

### Step 1: Understand the Definition of Efficiency
The efficiency (η) of a heat engine is defined as the ratio of the work output (W_net) to the heat input (Q_input):
\[ \eta = \frac{W_{net}}{Q_{input}} \]

### Step 2: Analyze the Maximum Efficiency
The maximum efficiency occurs when all the heat input is converted into work output. In this case:
\[ W_{net} = Q_{input} \]
Substituting this into the efficiency formula gives:
\[ \eta = \frac{Q_{input}}{Q_{input}} = 1 \]

### Step 3: Analyze the Minimum Efficiency
The minimum efficiency occurs when no work is produced from the heat input. In this case:
\[ W_{net} = 0 \]
Substituting this into the efficiency formula gives:
\[ \eta = \frac{0}{Q_{input}} = 0 \]

### Step 4: Determine the Range of Efficiency
From the analysis, we see that the efficiency (η) can vary from 0 (no work output) to 1 (maximum work output). Therefore, the possible range of efficiency values is:
\[ 0 \leq \eta \leq 1 \]

### Step 5: Choose the Correct Answer
Based on the range derived, the correct option is:
- Option 1: 0 to 1

### Final Answer
The value of η may lie between **0 and 1**.

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