CARNOT — CYCLE IN THERMODYNAMICS…

The Carnot Cycle

The Carnot cycle consists of the following four processes:

1. A reversible isothermal gas expansion process. In this process, the ideal gas in the system absorbs qin amount heat from a heat source at a high temperature Thigh ℎ, expands and does work on surroundings.
2. A reversible adiabatic gas expansion process. In this process, the system is thermally insulated. The gas continues to expand and do work on surroundings, which causes the system to cool to a lower temperature, T low.
3. A reversible isothermal gas compression process. In this process, surroundings do work to the gas at T low, and causes a loss of heat, q out.
4. A reversible adiabatic gas compression process. In this process, the system is thermally insulated. Surroundings continue to do work to the gas, which causes the temperature to rise back to T high ℎ.

The Carnot cycle is a theoretical thermodynamic cycle that is often used as a benchmark for comparing the efficiency of real-world heat engines. It was first proposed by French engineer Nicolas Léonard Sadi Carnot in 1824 and has since become a fundamental concept in the field of thermodynamics.

The Carnot cycle is an idealized cycle that consists of four reversible processes: two isothermal processes and two adiabatic processes. The cycle is often represented on a pressure-volume (PV) diagram, where the four processes are depicted as a closed loop. The following is a brief overview of each of the four processes in the Carnot cycle:

• Isothermal Expansion: In the first process, the working fluid (usually a gas) is heated isothermally at a high temperature, while the volume of the system increases. During this process, the system absorbs heat from a high-temperature reservoir and performs work.
• Adiabatic Expansion: In the second process, the working fluid expands adiabatically (i.e., without heat transfer) while its temperature decreases. This process results in a decrease in the pressure and volume of the system, and work is performed by the system.
• Isothermal Compression: In the third process, the working fluid is cooled isothermally at a low temperature while the volume of the system decreases. During this process, heat is released from the system to a low-temperature reservoir, and work is performed on the system.
• Adiabatic Compression: In the final process, the working fluid is compressed adiabatically, while its temperature increases. This process results in an increase in the pressure and decrease in the volume of the system, and work is performed on the system.
• The Carnot cycle is a reversible cycle, meaning that each of the four processes can be reversed to return the system to its original state. In practice, however, it is impossible to achieve a completely reversible cycle, and real-world heat engines operate on less efficient cycles.

The efficiency of the Carnot cycle is determined by the temperature difference between the high-temperature reservoir and the low-temperature reservoir. The maximum efficiency of the cycle can be calculated using the following equation:

Efficiency = 1 — (T_low/T_high)

where T_low is the temperature of the low-temperature reservoir and T_high is the temperature of the high-temperature reservoir. This equation shows that the efficiency of the Carnot cycle increases as the temperature difference between the two reservoirs decreases.

The Carnot cycle has important practical applications in the design of heat engines and refrigeration systems. The maximum efficiency of a heat engine is limited by the Carnot cycle, and real-world engines are designed to approach this maximum efficiency as closely as possible. Similarly, the coefficient of performance (COP) of a refrigeration system is determined by the Carnot cycle, and real-world systems are designed to have a COP as close to the Carnot COP as possible.

• In conclusion, the Carnot cycle is an idealized thermodynamic cycle that serves as a benchmark for comparing the efficiency of real-world heat engines and refrigeration systems. The cycle consists of four reversible processes, two isothermal processes, and two adiabatic processes, and the efficiency of the cycle is determined by the temperature difference between the high-temperature and low-temperature reservoirs. While the Carnot cycle is an idealization and cannot be perfectly achieved, it provides a useful theoretical framework for understanding the limits of heat engine efficiency and refrigeration system performance in Thermodynamics…
• The Carnot cycle is the ideal cycle against which all external combustion heat engines are usually compared, at least in the first instance. The Otto cycle is the corresponding ideal cycle for comparison with internal combustion engine designs. The Carnot cycle describes the maximum theoretical efficiency achievable with a perfect coolant and insulation properties with optimum working conditions. As an ideal cycle its performance cannot be replicated in Practise.
• The Carnot cycle describes the transfer of heat from a source to a sink wherein some of this energy is directed to perform useful work. The cycle comprises four individual stages: two of expansion and two of compression. The heat source is conventionally assigned a temperature T1 and the sink a temperature T2, where 1>2. Although it represents a theoretical optimum, a number of practical examples can be used to illustrate the principle of the Carnot cycle, given the corresponding efficiency cannot be achieved in reality. The most common example is a piston operating on a gaseous working substance in a cylinder, as shown in Fig. 7.3. Carnot envisaged the piston being the prime mover connected to a crank with which to supply the rotational motion necessary to lift a specified mass. The four stages of the Carnot cycle are as follows:

Some of the aforementioned issues can be eliminated by performing the Carnot vapor cycle in an alternative way as presented in Fig. 3. Nevertheless, the alternative Carnot vapor cycle comes with other problems such as isothermal heat transfer at variable pressures and isentropic compression to extremely high pressures. Therefore, it is stated that the Carnot vapor cycle cannot be approximated in actual vapor driven Systems.The Carnot cycle proved that in the steam-water cycle the lower the heat sink temperature the higher the cycle efficiency. This means the condenser pressure should be as low as possible. The condenser pressure is lowered to sub-atmospheric condition by evacuating air from the condenser shell as well as from the internal area of the connected LP turbine. This evacuation may be realized either by using a vacuum pump or with the help of a steam jet-air ejector. Either of these vacuum-creating devices sucks air from the condenser shell and discharges it to the atmosphere.

Steam to the ejector is supplied from the auxiliary steam header during all modes of operation. Condensed steam from the ejector is recycled back to the condensate system.

Prior to starting a steam turbine it is best to evacuate the LP turbine and condenser rapidly to reduce the condenser pressure from atmospheric to a lower value. This is achieved by using either a non-condensing type single-stage starting air ejector or a vacuum pump. The Heat Exchange Institute (HEI) recommends that for the evacuation of air from atmospheric pressure to 33.86 kPa absolute pressure Hg in about 1800 s the capacity of the evacuating equipment should be as given in Table 9.2. (Note: As per the HEI, the standard condition corresponds to pressure 101.3 kPa (14.7 psia) and temperature 294 K (70°F)).