Carnot Engine: Principles, Cycle Steps & Efficiency Explained

Carnot Engine: Principles, Cycle Steps & Efficiency

An in-depth look at the ideal heat engine and its maximum theoretical efficiency.

Table of Contents

• 1. Carnot’s Discovery & Modern View
• 2. Principles of the Carnot Engine
• 3. Carnot’s Theorem
• 4. Steps of the Carnot Cycle
• 5. Maximum Efficiency Formula
• 6. Significance & Applications
• 7. Conclusion

1. Carnot’s Discovery & Modern View

In 1824, Sadi Carnot proposed the Carnot cycle, an idealized reversible thermodynamic cycle. He showed that to produce mechanical work, heat must flow from a hot reservoir (temperature Th) to a cold reservoir (temperature Tc), with a working fluid undergoing reversible processes.

Carnot observed that the work output depends only on Th and Tc, not on the working substance (steam, gas, mercury, etc.).

2. Principles of the Carnot Engine

The Carnot engine is an ideal reversible heat engine. Key principles:

• Reversible processes maximize work output without losses.
• Efficiency depends only on reservoir temperatures.
• All reversible engines operating between the same Th and Tc have equal efficiency.

Real engines are irreversible, so they always have lower efficiency than the Carnot limit.

3. Carnot’s Theorem

Carnot’s theorem states:

• No engine can be more efficient than a reversible Carnot engine between the same two reservoirs.
• All reversible engines between the same Th and Tc share the same efficiency.

A reversible engine can act as a heat pump when run in reverse, transferring heat from cold to hot.

4. Steps of the Carnot Cycle

1. Isothermal expansion at Th: The working fluid absorbs heat QH from the hot reservoir while expanding reversibly at constant temperature Th, doing work on the surroundings.
2. Adiabatic expansion (Th → Tc): The fluid expands without heat exchange, causing its temperature to drop from Th to Tc.
3. Isothermal compression at Tc: The fluid rejects heat QC to the cold reservoir while being compressed reversibly at constant temperature Tc.
4. Adiabatic compression (Tc → Th): The fluid is compressed without heat exchange, raising its temperature back to Th, completing the cycle.

5. Maximum Efficiency Formula

The Carnot efficiency is:

η = 1 – (Tc / Th)

where Th and Tc are absolute temperatures of the hot and cold reservoirs. It represents the maximum fraction of heat converted to work.

No real engine can surpass this efficiency; all real engines have additional irreversibilities.

6. Significance & Applications

The Carnot engine sets the upper limit for thermal efficiency, guiding:

• Design of power plants and heat engines.
• Optimization of cycles in turbines, refrigerators, and heat pumps.
• Understanding irreversibilities and real-world losses.

Improving Th (higher combustion temperature) or lowering Tc (better cooling) raises potential efficiency, but material and practical limits apply.

7. Conclusion

The Carnot engine remains a foundational concept in thermodynamics. Its ideal cycle and efficiency formula provide the benchmark that all real heat engines strive toward but can never surpass.

Remember: Carnot’s ideal reversible cycle defines the maximum possible efficiency, highlighting the role of temperature difference and irreversibilities in real machines.