Carnot Cycle

Definition

The Carnot cycle is an idealized thermodynamic cycle that describes the maximum theoretical efficiency of a heat engine operating between two thermal reservoirs. It is named after the French engineer and physicist Sadi Carnot, who developed the concept in the 1820s as a way to understand the limitations of steam engines and other heat-based power sources.

5 Must Know Facts For Your Next Test

1. The Carnot cycle consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.
2. The efficiency of a Carnot cycle is determined solely by the temperatures of the hot and cold reservoirs, and is given by the formula: $\eta = 1 - T_c/T_h$, where $T_c$ is the temperature of the cold reservoir and $T_h$ is the temperature of the hot reservoir.
3. The Carnot cycle is the most efficient possible heat engine operating between two fixed temperatures, and all other heat engines are less efficient.
4. The Carnot cycle is an idealized model, and real-world heat engines always have some irreversible processes that reduce their efficiency compared to the Carnot cycle.
5. The second law of thermodynamics states that the efficiency of a heat engine can never exceed that of a Carnot cycle operating between the same two temperatures.

Review Questions

• Describe the four reversible processes that make up the Carnot cycle.
  • The Carnot cycle consists of four reversible processes: (1) Isothermal expansion, where the system absorbs heat from the hot reservoir and expands at a constant temperature; (2) Adiabatic expansion, where the system expands and cools without exchanging heat with the surroundings; (3) Isothermal compression, where the system rejects heat to the cold reservoir and is compressed at a constant temperature; and (4) Adiabatic compression, where the system is compressed and heated without exchanging heat with the surroundings. These four processes form a closed loop that represents the maximum theoretical efficiency of a heat engine operating between two thermal reservoirs.
• Explain how the efficiency of the Carnot cycle is determined by the temperatures of the hot and cold reservoirs.
  • The efficiency of the Carnot cycle is given by the formula $\eta = 1 - T_c/T_h$, where $T_c$ is the temperature of the cold reservoir and $T_h$ is the temperature of the hot reservoir. This formula shows that the efficiency of the Carnot cycle depends solely on the temperatures of the two reservoirs, and not on the working substance or other details of the engine. The higher the temperature difference between the hot and cold reservoirs, the greater the efficiency of the Carnot cycle. This is because a larger temperature difference allows for more work to be extracted from the heat transfer process.
• Discuss the significance of the Carnot cycle in the context of the second law of thermodynamics.
  • The Carnot cycle is significant because it represents the maximum theoretical efficiency of a heat engine operating between two fixed temperatures, as stated by the second law of thermodynamics. The second law states that the efficiency of any real-world heat engine will always be less than that of a Carnot cycle operating between the same two temperatures. This is because the Carnot cycle is an idealized, reversible process, while real-world engines always have some irreversible processes, such as friction and heat transfer, that reduce their efficiency. The Carnot cycle, therefore, serves as a benchmark for evaluating the performance of actual heat engines and understanding the fundamental limits of thermodynamic efficiency.

Related terms

Thermodynamics: The study of the relationships between heat, work, temperature, and energy in systems.

Entropy: A measure of the disorder or randomness in a system, which increases as a system becomes less organized.

Heat Engine: A device that converts thermal energy into mechanical work, such as a steam engine or internal combustion engine.