Question

Why is the heat engine not 100% efficient?

Answer 1

Concept

According to Carnot's theorem which states that:

1. Any heat engine which is operating between two hot reservoirs is not as efficient as a Carnot engine operating between the same hot reservoirs.
2. The efficiency of any heat engine is limited due to temperature.
3. According to Carnot's theorem maximum efficiency of an engine can be given as:

${\eta }_{max}=W/Q_H=1-T_C/T_H$

Where, $W$ = work done by the system,

$Q_{H_{}}$= heat energy put into the system,

$T_C$ = absolute temperature of the cold reservoir,

$T_H$ = absolute temperature of the hot reservoir.

Explanation

1. From the above equation, we can say that the maximum efficiency of any heat engine depends on the temperature difference between a hot reservoir and a cold reservoir.
2. The system's efficiency will be higher when this temperature difference is maximum.
3. For a heat engine efficiency to be $100\%$ cold reservoir temperature should be 0 K, which is impossible practically.
4. A heat engine is said to be $100\%$ efficient when all the heat energy taken by the engine is converted into some useful work or mechanical energy.
5. Since a heat engine cannot convert all the heat energy into useful work so its efficiency can never be $100\%$.
6. So practically, it is not possible for a heat engine to achieve $100\%$efficiency.

Thus, the heat engine is not $100\%$ efficient.