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Carnot Engine

Definition: Whatis the Carnot Engine?

Carnot engine is an analytical engine that operates on a reversible thermodynamic cycle. It gives the maximum possible efficiency that a heat engine can possess. In a thermodynamic cycle,a system is taken through several stages before returning to its starting initial stage. During this process, the system exchanges heat with the surroundings, and it performs work. The surroundings consist of two reservoirs, one hot and another cold, that can store a vast amount of heat. They have high heat capacities and are kept at constant temperatures.

Carnot Engine Diagram

The Carnot engine was devised by French engineer and scientist Nicolas Léonard Sadi Carnot in 1824.

Carnot Engine Cycle

The working of the Carnot engine can be understood by studying its cycle of operations, calledthe Carnot engine cycle or Carnot cycle. It is areversible closed thermodynamic cycle in which an ideal gas kept inside a cylinder with a piston on its top is taken through a series of four successive operations. The sequence of steps in a Carnot cycle is as follows.

  1. Isothermal expansion: The system takes heat from the hot reservoir, and the gas expands isothermally. During this process, the pressure decreases, and the volume increases, while the temperature remains constant at T1.
  2. Adiabatic expansion: The gas is allowed to expand adiabatically, which means that there is no exchange of heat between the system and the surroundings. Here, the temperature decreases to T2, the pressure drops down, and the volume increases slightly.
  3. Isothermal compression: The gas is compressed isothermally. Heat escapes from the system into the surrounding and is dumped into the cold reservoir. The temperature remains constantat T2. The pressure increases while the volume decreases.
  4. Adiabatic compression: Pressure is applied to the gas such that the volume decreases further. The gas is isolated so that there is no exchange of heat between the system and the surroundings. This process increases the temperature back to T1.

During the working of Carnot engine, the system is taken from temperature T1 to T2 and then back from temperature T2 to T1.It is best represented by a pressure-volume (PV) diagram.

Carnot Engine Cycle

Carnot Refrigerator

The thermodynamic cycle that is observed in the Carnot engine is a reversible process. The engine can be acted upon by an external force to transfer heat. Thus, the Carnot engine workslike a refrigerator.Heat is sucked out of the cold reservoir that is present inside a fridge. Electrical energy (work input)is supplied from the wall outlet.There is also some waste-heatdumped into the kitchen (surrounding).

Efficiency of Carnot Engine

All heat engines perform work and are defined by their efficiencies. In physics, efficiency is defined as the ratio of work done (W) to the amount of heat taken in by the system (Qh).

η = W/Qh = (Qh – Qc)/Qh

Qc is the heat that is wasted and dumped into the cold reservoir. The following formula gives the efficiency of a Carnot engine.

η = 1 – T2/T1

The conceptual thinking of the Carnot cycle is that it establishes the maximum possible efficiency for any heat engine cycle operating between T1 and T2.The reason is that there is no friction between the piston and the walls of the cylinder.It runs on reversible processes, which yields maximum work output for given heat input. However, the Carnot engine cannot achieve 100% thermal efficiency because some waste heat is always produced during its operation.

Principle of Carnot Engine or Carnot Theorem

The principle of Carnot engine, also called Carnot theorem, states that “Any system working between two given temperatures T1 (hot reservoir) and T2(cold reservoir), can never have an efficiency more than the Carnot engine working between the same reservoirs respectively.”

Carnot Engine Entropy

Another useful quantity that measures the disorder of the system is the entropy. It is the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work. Since the Carnot cycle is a reversible process, its entropy change is zero.

Carnot Engine Entropy

Applications of Carnot Engine

Carnot engine is practical in many applications in thermal devices and thermal machines,mostly because they require a temperature gradient to do mechanical work. Here are some of the applications, including in real-world modeling.

  • To evaluate real engines in the context of their theoretical maximum efficiency, especially during the design
  • As a theoretical reference cycle to compare the efficiencies of the actual Otto (petrol) or Diesel cycles
  • To convert oceanic thermal energy into work 

However, the Carnot engine is not a practical engine cycle because the heat transfer into the engine in the isothermal process is too slow to be of practical value.

Carnot Engine Animation

Carnot Engine Applet

Applet Courtesy: University of Virginia

Article was last reviewed on Saturday, July 25, 2020

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