carnot cycle explained: with P-v, T-S diagram and formulas

 The Carnot cycle is a theoretical thermodynamic cycle that provides an idealized model for the most efficient heat engine possible. Named after the French physicist Sadi Carnot, it sets a standard for all real heat engines. The cycle consists of four reversible processes:

1-2 Isothermal Expansion:

• Process: The gas (usually an ideal gas) is placed in contact with a hot reservoir at a constant temperature $T_H$.
• Action: The gas absorbs heat $Q_H$ from the reservoir, causing it to expand.
• Work Done: The gas does work on the environment by pushing up a piston.

2-3 Adiabatic Expansion:

• Process: The system is insulated, so no heat is exchanged with the surroundings.
• Action: The gas continues to expand, doing work on the piston, and its temperature decreases from $T_H$ to $T_C$ (the temperature of the cold reservoir).
• Result: The internal energy of the gas decreases.

3-4 Isothermal Compression:

• Process: The gas is brought into contact with a cold reservoir at a constant temperature $T_C$.
• Action: The gas releases heat $Q_C$ to the cold reservoir as it is compressed.
• Work Done: The environment does work on the gas to compress it.

4-1 Adiabatic Compression:

• Process: Again, the system is insulated, so no heat is exchanged.
• Action: The gas is compressed further, and its temperature rises from $T_C$ back to $T_H$.
• Result: The internal energy of the gas increases as work is done on it.

Efficiency of the Carnot Cycle

The efficiency $\eta$ of a Carnot engine is given by:

$$\eta =1-\frac{T_C}{T_H}$$

where:

• $T_H$ is the absolute temperature of the hot reservoir.
• $T_C$ is the absolute temperature of the cold reservoir.

Key Points

• Reversibility: The Carnot cycle is an ideal cycle that assumes all processes are reversible and no energy is lost to friction or other irreversibility's.
• Limitations: In practice, no real engine can achieve the efficiency of a Carnot engine due to irreversible processes and practical limitations.
• Significance: The Carnot cycle demonstrates the fundamental principles of thermodynamics and establishes the maximum possible efficiency for heat engines operating between two temperature reservoirs.

If you have specific aspects of the Carnot cycle that you want to explore further, feel free to ask!