Even Carnot engine cannot give `100%` efficiency because we cannot

Options

A. prevent radiation
B. find ideal sources
C. reach absolute zero temperature
D. eliminate friction

Explanation

To solve the question regarding why a Carnot engine cannot achieve 100% efficiency, we can follow these steps:

### Step 1: Understand the Carnot Engine
The Carnot engine is a theoretical engine that operates on the Carnot cycle, which is the most efficient cycle possible for a heat engine. Its efficiency depends on the temperatures of the hot and cold reservoirs.

### Step 2: Write the 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 hot reservoir,
- \(T_2\) is the absolute temperature of the cold reservoir.

### Step 3: Set the Condition for 100% Efficiency
For the Carnot engine to have 100% efficiency (η = 1), we can set up the equation:
\[ 1 = 1 - \frac{T_2}{T_1} \]
This simplifies to:
\[ \frac{T_2}{T_1} = 0 \]
This implies that \(T_2\) must be 0 K (absolute zero).

### Step 4: Understand the Implications of Absolute Zero
Absolute zero (0 K) is the theoretical temperature at which all molecular motion ceases. According to the third law of thermodynamics, it is impossible to reach absolute zero in a finite number of steps. Therefore, \(T_2\) cannot be 0 K.

### Step 5: Conclusion
Since it is impossible to reach absolute zero, the Carnot engine cannot achieve 100% efficiency. The presence of a finite temperature for the cold reservoir (greater than 0 K) means that there will always be some waste heat, preventing 100% efficiency.

### Summary
The reason a Carnot engine cannot give 100% efficiency is that it requires the cold reservoir to be at absolute zero (0 K), which is unattainable.

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