Question

In an engine cycle like the one shown in Figure 

 

heat is added over a range of temperatures. Explain why even if it were run reversibly, its efficiency would be less than the Carnot limit defined by the high- and low-temperature set points and shown in the figure ( ηC = T₄-T₂)/T₄. Is this in itself a disadvantage of such a cycle?

 

 

Answer 1

Carnot engines are heat engines that are known to have maximum efficiency. The working fluid of this engine is compressed isothermally at lower temperature, compressed adiabatically to a higher temperature, expanded isothermally at higher temperature and expanded adiabatically to the lower temperature.

 

Even though Carnot engines attain maximum efficiency, these engines are highly impractical. In such an unrealistic heat engine, extreme pressure and volume is used, but only a small amount of work is done per cycle. In case of a practical engine, the cycle is irreversible at isothermal conditions. Hence, they would attain lower efficiency than a Carnot engine.

 

The efficiency of Carnot cycle (ncarnot) is given by,

 

Here, T is the temperature of the sink or the environment and T. is the temperature of the source or the reservoir.

 

When heat is added from a source of thermal energy to a practical heat engine like the hypothetical heat engine shown in figure 10.3, the working fluid expands and does some work. Even after heat is no longer supplied to the engine, the gas continues to expand and hence, more work is done by the system. Thus, the temperature of the system drops. So, efficiency of this heat engine is lowered, compared to the Carnot engine.

 

Since Carnot heat engine is not practical to use, comparing practical heat engines with Carnot engines is not necessary. Hence, having a low efficiency than Carnot efficiency is not a disadvantage for such practical heat engines.

 

 

Disadvantage or not:

Therefore, practical heat engine cycles such as the one shown in figure 10.3 is less efficient than a Carnot cycle because more work is done by practical heat engines than Carnot engines, and hence, the temperature drops. It is not a disadvantage of such practical engines, because attaining maximum efficiency while doing more work is practically impossible.

Carnot engines are heat engines that are known to have maximum efficiency.