## Carnot Engine – Class 11 | Chapter – 12 | Physics Short Notes Series PDF for NEET & JEE

Carnot Engine: A Carnot engine is a theoretical engine that operates on the Carnot cycle, a thermodynamic cycle that is reversible and operates between two heat reservoirs at different temperatures. It is named after French physicist Sadi Carnot, who proposed the cycle in 1824 as a theoretical model of a heat engine that operates with maximum efficiency.

The Carnot engine consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. It operates by taking in heat energy from a high-temperature reservoir, converting some of that energy into mechanical work, and expelling the remaining energy to a low-temperature reservoir.

The Carnot engine is a theoretical construct, and no engine can actually achieve its maximum efficiency because of losses due to friction and other factors. However, the Carnot cycle provides a useful model for understanding the limits of engine efficiency and for comparing the performance of real-world engines.

## Carnot Theorem

Carnot’s theorem, also known as Carnot’s principle, is a fundamental principle in thermodynamics that states that the efficiency of any reversible heat engine is solely determined by the temperatures of the heat source and heat sink, and is independent of the working substance used in the engine.

This principle was first proposed by French physicist Sadi Carnot in 1824 as a theoretical result of his analysis of the maximum efficiency of a heat engine. Carnot showed that the efficiency of an ideal reversible heat engine, operating between two heat reservoirs at temperatures T1 and T2, is given by:

η = 1 – T2/T1

where η is the efficiency of the engine, expressed as a fraction or percentage. This means that the maximum possible efficiency of a heat engine is limited by the ratio of the temperatures of the heat source and heat sink, and that this maximum efficiency can only be achieved by a reversible engine.

Carnot’s theorem is important in the design and analysis of thermal systems, as it provides a fundamental limit on the performance of any heat engine, and helps to identify the most efficient designs for a given set of operating conditions. It also highlights the importance of reversible processes in thermodynamics, which are characterized by the absence of any irreversibilities or losses in energy.

## Carnot Cycle

The Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: two isothermal processes and two adiabatic processes. It is named after French physicist Sadi Carnot, who introduced it in 1824 as a theoretical model of a heat engine that operates with maximum efficiency.

The Carnot cycle operates between two heat reservoirs at different temperatures, a hot reservoir at temperature T1 and a cold reservoir at temperature T2. The four processes of the cycle are:

• Isothermal Expansion: The working substance (usually a gas) is placed in contact with the hot reservoir and allowed to expand slowly while absorbing heat from the reservoir at a constant temperature T1.
• Adiabatic Expansion: The working substance continues to expand, but now without gaining or losing heat from the surroundings, so the process is adiabatic. As the gas expands, it does work on the surroundings, decreasing its internal energy and temperature.
• Isothermal Compression: The working substance is now placed in contact with the cold reservoir and compressed slowly while releasing heat to the reservoir at a constant temperature T2.
• Adiabatic Compression: The working substance is compressed further, but now without exchanging heat with the surroundings, so the process is adiabatic. As the gas is compressed, work is done on it, increasing its internal energy and temperature.

The Carnot cycle is a reversible cycle, meaning that it can be run in reverse to act as a refrigeration cycle. The cycle is often depicted on a pressure-volume (PV) diagram, where the isothermal processes are represented by horizontal lines and the adiabatic processes are represented by sloping lines. The area enclosed by the cycle on the PV diagram represents the net work done by the engine.

The Carnot cycle is a theoretical ideal and no engine can achieve 100% efficiency, but it provides a useful benchmark for comparing the performance of real engines and for understanding the limits of thermodynamic efficiency.

## Applications of Carnot Cycle

The Carnot cycle is a theoretical ideal, and no engine can achieve 100% efficiency. However, the Carnot cycle provides a useful benchmark for understanding the limits of thermodynamic efficiency and comparing the performance of real engines. Some applications of the Carnot cycle are:

• Steam power plants: Steam power plants are commonly used to generate electricity. The heat source in the power plant is a furnace that burns coal or natural gas to produce heat. The heat is then used to boil water and produce steam, which expands through a turbine to generate electricity. The cold sink in the power plant is the atmosphere or a nearby river, which absorbs waste heat from the power plant. The Carnot cycle provides a useful benchmark for evaluating the efficiency of the power plant and optimizing its performance.
• Refrigeration and air conditioning: Refrigeration and air conditioning systems are used to cool buildings and preserve food and medicine. The Carnot cycle provides a useful benchmark for evaluating the efficiency of these systems and optimizing their performance.
• Heat pumps: Heat pumps are used to heat buildings and swimming pools. The Carnot cycle provides a useful benchmark for evaluating the efficiency of heat pumps and optimizing their performance.
• Internal combustion engines: Internal combustion engines are used in cars, trucks, and airplanes to convert fuel into mechanical energy. The Carnot cycle provides a useful benchmark for evaluating the efficiency of internal combustion engines and optimizing their performance.

In summary, while no engine can achieve 100% efficiency, the Carnot cycle provides a useful benchmark for understanding the limits of thermodynamic efficiency and optimizing the performance of various thermal systems.

## Limitations of Carnot Engine (Cycle)

The Carnot cycle is a theoretical ideal and no engine can achieve 100% efficiency. While the Carnot cycle is a useful benchmark for understanding the limits of thermodynamic efficiency and comparing the performance of real engines, it has some limitations that must be considered:

• Assumption of reversible processes: The Carnot cycle assumes that all the processes involved are reversible, which means that there are no irreversibilities or losses of energy. In real engines, there are always some losses due to friction, heat transfer, and other irreversibilities, which reduce the efficiency of the engine.
• Ideal gas assumption: The Carnot cycle assumes that the working substance is an ideal gas, which means that it has no intermolecular forces and occupies no volume. In reality, most working substances have intermolecular forces, and their volume cannot be ignored, which can affect the efficiency of the engine.
• Constant temperature assumption: The Carnot cycle assumes that the heat transfer occurs at constant temperatures. In reality, heat transfer occurs over a range of temperatures, which can affect the efficiency of the engine.
• Practical limitations: The Carnot cycle is a theoretical ideal, and there are practical limitations to its implementation. For example, the compression and expansion processes must be carried out slowly to maintain reversibility, which can be impractical in some applications.

In summary, while the Carnot cycle is a useful benchmark for understanding the limits of thermodynamic efficiency and comparing the performance of real engines, it has some limitations that must be considered in practical applications.

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