Even carnot heat engine cannot give `100%` efficiency. Explain why
OR
can you design a heat engine of `100%` efficiency? Explain ypur answer.
OR
A heat engine with `100%` efficiency is only a theoretical possibility. Explain.

Answer

To explain why a Carnot heat engine cannot achieve 100% efficiency, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Heat Engines**: A heat engine operates by transferring heat from a high-temperature reservoir (T1) to a low-temperature reservoir (T2) and converting some of that heat into work (W).

2. **Efficiency Definition**: The efficiency (η) of a heat engine is defined as the ratio of the work output (W) to the heat input (Q1) from the high-temperature reservoir. Mathematically, it is expressed as:
\[ \eta = \frac{W}{Q_1} = 1 - \frac{Q_2}{Q_1} \]
where Q2 is the heat rejected to the low-temperature reservoir.

3. **Carnot Efficiency Formula**: For a Carnot engine, which is an idealized engine operating between two temperature reservoirs, the efficiency can be expressed in terms of the absolute temperatures (in Kelvin) of the reservoirs:
\[ \eta_{Carnot} = 1 - \frac{T_2}{T_1} \]
where T1 is the temperature of the hot reservoir and T2 is the temperature of the cold reservoir.

4. **Condition for 100% Efficiency**: For the efficiency to be 100% (η = 1), the term \(\frac{T_2}{T_1}\) must equal 0. This implies:
\[ T_2 = 0 \quad \text{or} \quad T_1 \to \infty \]

5. **Impossibility of Absolute Zero**: Achieving a temperature of absolute zero (0 Kelvin) is impossible according to the third law of thermodynamics. Therefore, T2 cannot be zero.

6. **Limitations on Temperature**: Additionally, it is not feasible to have an infinite temperature (T1). All real materials have limitations on how high their temperature can be raised.

7. **Conclusion**: Since both conditions (T2 = 0 and T1 = ∞) cannot be satisfied in reality, a heat engine, including the Carnot engine, cannot achieve 100% efficiency. Therefore, 100% efficiency is only a theoretical possibility and cannot be realized in practice.