Assertion: Efficiency of a heat engine can't be greater than efficiency of Carnot engine.
Reason: Effieciency of any engine is never 100%

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To analyze the given assertion and reason, let's break down the problem step by step.

### Step 1: Understand the Assertion
The assertion states that "the efficiency of a heat engine can't be greater than the efficiency of a Carnot engine."

**Explanation:**
- The Carnot engine is an idealized engine that operates between two heat reservoirs at temperatures \( T_H \) (hot reservoir) and \( T_C \) (cold reservoir).
- The efficiency of a Carnot engine is given by the formula:
\[ \eta_{Carnot} = 1 - \frac{T_C}{T_H} \]
- According to the second law of thermodynamics, no real engine can be more efficient than a Carnot engine operating between the same two temperatures.

### Step 2: Understand the Reason
The reason states that "the efficiency of any engine is never 100%."

**Explanation:**
- The efficiency of an engine is defined as the ratio of useful work output to the heat input. It can be expressed as:
\[ \eta = 1 - \frac{Q_C}{Q_H} \]
where \( Q_C \) is the heat rejected to the cold reservoir and \( Q_H \) is the heat absorbed from the hot reservoir.
- For an engine to have 100% efficiency, it would mean that no heat is rejected (\( Q_C = 0 \)), which is impossible according to the laws of thermodynamics. Therefore, the efficiency of any real engine is always less than 100%.

### Step 3: Conclusion
- The assertion is **true** because the efficiency of any heat engine cannot exceed that of a Carnot engine.
- The reason is also **true** because the efficiency of any real engine is never 100%.

### Final Answer
Both the assertion and the reason are true, but the assertion is a broader statement about heat engines in general, while the reason explains a specific limitation of real engines.