What is Carnot engine?

Short Answer

A Carnot engine is an ideal heat engine that operates on the Carnot cycle and gives the maximum possible efficiency for converting heat into work. It works between two temperature reservoirs—one hot and one cold—and performs four reversible processes: two isothermal and two adiabatic.

The Carnot engine is not a real machine but a theoretical model used to understand the upper limit of efficiency. It helps compare real heat engines with the ideal standard of performance.

Detailed Explanation :

Carnot Engine

A Carnot engine is a theoretical heat engine invented by Sadi Carnot. It operates on the Carnot cycle, which consists of four perfectly reversible processes. This engine is considered the most efficient heat engine that can ever operate between two fixed temperatures. Although no real engine can be a perfect Carnot engine due to practical limitations, the concept is extremely important because it defines the maximum efficiency that any heat engine can achieve.

The Carnot engine works using a working substance—often considered an ideal gas—to absorb heat from a hot reservoir, do mechanical work, and release heat to a cold reservoir. The complete cycle returns the working substance to its initial state.

Working of a Carnot Engine

A Carnot engine performs four reversible processes, forming one complete cycle. These processes are:

  1. Isothermal Expansion at High Temperature (T₁)
  • The gas is allowed to expand at constant high temperature.
  • Heat Q₁ is absorbed from the hot reservoir.
  • The gas does work on the surroundings, increasing its volume.
  • Temperature remains constant because heat is supplied throughout the expansion.
  1. Adiabatic Expansion
  • After the isothermal expansion, the gas continues to expand, but no heat is exchanged.
  • The gas does work during this expansion, causing its temperature to fall from T₁ to T₂.
  • This prepares the gas for the next isothermal process.
  1. Isothermal Compression at Low Temperature (T₂)
  • The gas is compressed at constant low temperature.
  • The gas releases heat Q₂ to the cold reservoir.
  • Work is done on the gas.
  • Temperature remains constant due to heat rejection.
  1. Adiabatic Compression
  • The gas is compressed further without heat exchange.
  • The temperature rises from T₂ back to T₁.
  • The gas returns to its initial state, completing the cycle.

These four steps together form the Carnot cycle, which is the working principle of a Carnot engine.

Diagram Description (Conceptual)

On a pressure–volume (PV) graph:

  • Two isothermal curves represent heat absorption and rejection.
  • Two adiabatic curves are steeper and show temperature change.
  • The closed loop on the diagram represents the work done by the engine in one cycle.

Efficiency of a Carnot Engine

The efficiency of a Carnot engine is given by:

η = 1 − (T₂ / T₁)

Where,

  • T₁ = temperature of hot reservoir
  • T₂ = temperature of cold reservoir
  • Temperatures must be in Kelvin

This formula shows two important points:

  1. Higher hot temperature (T₁) increases efficiency.
  2. Lower cold temperature (T₂) also increases efficiency.

No real engine can exceed the efficiency of a Carnot engine operating between the same temperatures.

Significance of Carnot Engine

The Carnot engine is important because:

  1. Sets the Maximum Efficiency Limit

Real engines can only approach this limit but never exceed it.

  1. Basis of the Second Law of Thermodynamics

It clarifies that no engine can have 100% efficiency.

  1. Ideal Standard for Comparison

Engineers use Carnot efficiency to compare actual engines and measure their effectiveness.

  1. Demonstrates Reversible Processes

It shows how an ideal reversible engine would function without friction or heat loss.

  1. Helps in Designing Practical Engines

Although not achievable, its principles guide improvements in real machines.

Why a Carnot Engine Cannot Be Built in Practice

Even though a Carnot engine is perfect in theory, real-world limitations make it impossible to build:

  • No process is fully reversible.
  • Perfect insulation during adiabatic steps is impossible.
  • Real gases do not behave like ideal gases.
  • Friction in moving parts causes energy loss.
  • Heat transfer cannot occur infinitely slowly as required.

Therefore, a Carnot engine remains an idealized model, not a physical machine.

Applications of Carnot Engine Concept

While a Carnot engine itself is not used, its concept is applied in:

  • Power plant design
  • Refrigerator efficiency analysis
  • Heat pump performance
  • Engineering thermodynamics
  • Improving heat engine cycles

Engineers improve machines by reducing temperature losses and minimizing irreversibility, aiming to approach Carnot-like performance.

Conclusion

A Carnot engine is an ideal heat engine that operates on the Carnot cycle and represents the highest possible efficiency achievable between two temperature reservoirs. It absorbs heat, performs work, and rejects heat through reversible processes. Although it cannot be created in real life, it serves as a perfect benchmark to measure and improve the performance of practical engines. Understanding the Carnot engine helps explain the fundamental limits placed by thermodynamics on the conversion of heat into work.