21.7:
The Carnot Cycle
The Second Law of Thermodynamics states that no heat engine can have 100% efficiency. To derive the maximum theoretical efficiency, Sadi Carnot developed a hypothetical heat engine.
Since work is lost as heat in all irreversible processes, maximizing the efficiency of a heat engine means avoiding all irreversible processes.
However, heat flow through a finite temperature drop is an irreversible process. Hence, heat exchange between the engine and the hot and cold reservoirs must be isothermal. Moreover, when its temperature changes, it must change adiabatically.
In a Carnot cycle, the working fluid is assumed to be an ideal gas. First, it undergoes isothermal expansion in thermal contact with a heat reservoir at temperature T–h and absorbs heat Q–h.
The fluid then expands adiabatically, and its temperature drops to the temperature of the cold reservoir, T-c.
Next it is placed in contact with the cold reservoir at temperature T-c and compressed isothermally, rejecting heat Q–c.
Finally, the gas is thermally isolated and compressed adiabatically to reach its initial state at temperature T–h, thus completing the cycle.
21.7:
The Carnot Cycle
Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The French engineer Sadi Carnot devised a hypothetical cycle between the same two hot and cold reservoirs to deduce the limit. This theoretical cycle helps to understand the conventional cyclical systems’ performance limits in transforming heat to work. It also helps define an ideal reversible process via Carnot’s Principle.
The Carnot cycle plays a significant role in developing an important statement of the second law of thermodynamics. Since only two reservoirs are involved in its operation, along with the second law of thermodynamics, it can also be used to define an absolute temperature scale that is truly independent of any substance used for temperature measurement.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 20.6; page 663.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 4.5; page 155.