As a thermodynamics expert with a deep understanding of the principles governing heat engines, I can provide a comprehensive explanation regarding the efficiency of these machines. The question of whether a heat engine can have an efficiency of 100% is a fundamental one in the field of thermodynamics and touches upon the second law of thermodynamics, which is a cornerstone of physics.

Step 1: English Answer

The second law of thermodynamics is a principle that governs the direction of energy flow and the conversion of heat into work. It states that heat cannot spontaneously flow from a colder body to a hotter body, and it also implies that no heat engine can be perfectly efficient. The efficiency of a heat engine, denoted by \( \eta \), is the ratio of the work done (W) to the heat input (Q_in), which can be expressed as:

\[ \eta = \frac{W}{Q_{\text{in}}} \]

In an ideal scenario, if a heat engine could convert all the heat input into work, its efficiency would be 100%. However, the second law of thermodynamics dictates that this is not possible. The reason for this limitation lies in the concept of entropy, which is a measure of the disorder or randomness of a system. The second law states that the total entropy of an isolated system can never decrease over time, and processes that occur naturally tend to increase the total entropy.

When considering a heat engine, the entropy change during the conversion of heat into work is crucial. In a reversible process, which is a theoretical construct where the system can be returned to its initial state without any change in the entropy of the surroundings, the efficiency of a heat engine can be determined by the Carnot efficiency. The Carnot efficiency, denoted by \( \eta_C \), is given by:

\[ \eta_C = 1 - \frac{T_c}{T_h} \]

Here, \( T_c \) is the absolute temperature of the cold reservoir, and \( T_h \) is the absolute temperature of the hot reservoir. The temperatures must be measured in the same units, typically Kelvin (K).

Even in a Carnot engine, which is an idealized, reversible heat engine, the efficiency is less than 100% because the temperatures of the cold and hot reservoirs are different. In the real world, no engine can operate as a Carnot engine due to friction, heat conduction, and other irreversibilities that increase the entropy of the system and reduce efficiency.

Furthermore, the Kelvin-Planck statement of the second law specifically addresses the efficiency of heat engines. It asserts that it is impossible for any system to operate in a thermodynamic cycle and provide a net output of energy by complete conversion of heat from a single reservoir. This means that a heat engine cannot convert all the heat it absorbs from a single heat source into work without producing other effects, such as transferring some heat to a cooler reservoir.

In conclusion, while the concept of a heat engine with 100% efficiency is theoretically intriguing, it is physically impossible according to the second law of thermodynamics. All real heat engines operate with efficiencies far below 100% due to the inherent limitations imposed by the laws of physics and the practical constraints of engineering and materials science.

**read more >>

The second law of thermodynamics puts a fundamental limit on the thermal efficiency of all heat engines. Even an ideal, frictionless engine can't convert anywhere near 100% of its input heat into work. ... No device converting heat into mechanical energy, regardless of its construction, can exceed this efficiency.read more >>