Carnot Engine

Carnot Engine - Working and Efficiency

Carnot engine is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824. Carnot states that a hot body is required that generates heat and a cold body to which the caloric is conveyed, which produces a mechanical work in the process. It also states that said work is free of the material that is used to create heat and the construction and design material of the machine.

Modern diagram

The above figure displays a block diagram of a general heat engine, like the Carnot engine. In the diagram, the “working body”, a word presented by Clausius in 1850, can be any vapor or fluid body through which heat “Q can be transmitted to yield work. Carnot had proposed that the fluid body could be any material capable of expansion, such as vapor of alcohol, the vapor of mercury, the vapor of water, a permanent air or gas etc. While, in these initial years, engines came in a number of patterns, usually QH was delivered by a boiler, wherein water was boiled over a heater; QC was usually delivered by a stream of cold flowing water in the form of a condenser situated on a separate part of the engine. The yield work, W, denotes the movement of the piston as it is used to rotate a crank-arm, which in turn was normally used to power a pulley so as to lift water out of submerged salt mines. Carnot states work as “weight lifted through a height”

Carnot Engine Principles

Carnot principles are just for cyclical devices such as heat engines, which state that:

• • The effectiveness of an irreversible heat engine is always less than the efficiency of a reversible one functioning between the similar two reservoirs.

• • The effectiveness of all reversible heat engines working between the similar two reservoirs is equal.

• To escalate the thermal efficiency of a gas power turbine, it is essential to increase the temperature of the combustion room. such as, turbines blades cannot hold out the high-temperature gas and which will eventually lead to early fatigue.
Carnot’s Theorem

This theorem defines that no engine functioning between two known temperatures can be more effective than a reversible engine functioning between the similar two temperatures and that all the reversible engines functioning between the same two temperatures have the similar efficiency, whatever the working material might be. As per the Carnot theorem, the reversible engine will always have greater productivity than the irreversible one. The reversible heat engine works on a reverse cycle and behaves as a heat pump.

The Efficiency of Carnot’s Cycle

The Carnot cycle is reversible signifying the upper limit on the efficiency of an engine cycle. Practical engine cycles are irreversible and therefore have inherently much lower efficiency than the Carnot efficiency when working at similar temperatures. One of the factors determining efficiency is the addition of the working fluid in the cycle and its removal. The Carnot cycle reaches maximum efficiency because all the heat is pushed to the working fluid at the maximum temperature.

Carnot cycle

Steps in cycle

Step 1 Isothermal expansion.

Image 1

Heat is passed reversibly from the high-temperature pool at fixed temperature TH (isothermal heat absorption). In this step (1 to 2 on image 1, A to B in image 2) the gas is allowed to expand, doing work on the surroundings by pushing up the piston (stage 1 figure, right). Even though the pressure drops from points 1 to 2 (image 1) the temperature of the gas does not alter in the process because it is in thermal contact with the hot pool at Th, and therefore the expansion is isothermal. Heat energy Q1 is absorbed from the high-temperature pool resulting in an increase in the entropy of the gas by the amount. {\displaystyle \Delta S_{1}=Q_{1}/T_{h}}

Image 2

Expansion of the gas. In this step (2 to 3 on image 1, B to C in image 2) the gas in the engine is thermally shielded from both the hot and cold pools. Thus they cannot gain nor lose heat, so it called an 'adiabatic' process. The gas rises to expand by the drop in pressure, doing work on the surroundings (raising the piston; stage 2 figure, above), and losing a volume of internal energy similar to the work done. The gas begins to expansion without heat input causes it to cool to the "cold" temperature, Tc. The entropy remains the same.

Step 3 Isothermal Compression.

Image 3

Heat shifted reversibly to a low-temperature pool at constant temperature TC. (isothermal heat elimination) (3 to 4 on image 1, C to D on image 2) Now the gas in the engine is in thermal contact with the cold pool at temperature Tc. The surroundings do work on the gas, by pushing the piston down (stage 3 image, above), causing a volume of heat energy Q2 to leave the system to a low-temperature pool and the entropy of the system to decline by the amount. (This is the equal amount of entropy absorbed in step 1, as can be observed from the Clausius inequality.)

Once again the gas in the engine is thermally shielded from the hot and cold pools, and the engine is expected to be frictionless, therefore it is reversible. In this step, the surroundings do work on the gas, pushing the piston down more (stage 4 image, above), rising it's internal energy, compressing it, and producing its temperature to rise back to Th due only to the work added to the system, but the entropy remains the same. At this stage, the gas is in the same state as at the beginning of the step.

Therefore, the total work done by the gas on the environment in one complete cycle is shown by

As step 2–>3 is an adiabatic process, we can write T1V2Ƴ-1 = T2V3Ƴ-1
or

Equally, for process 4–>1, we can write

This indicates,

So, the expression for a net efficiency of Carnot engine decreases to:

The Carnot engine cycle when behaving as a heat engine contains the following steps:

• • Reversible or changeable isothermal compression of the gas at the “cold” temperature.

• • Isentropic compression of the gas

• • Reversible or changeable adiabatic (Isentropic) expansion of the gas.

• • Reversible or changeable isothermal expansion of the gas at the “hot” temperature.

• Applications of the Carnot Cycle

Thermal machines or thermal devices are one of the applications of the Carnot cycle. The heat pumps to generate heating, the refrigerators to yield cooling, the steam turbines used in the ships, the combustion engines of the combustion vehicles and the reaction turbines of an airplane are some of the examples that we can give.

Limitations

This equation shows that the bigger the temperature range, the more effective is the cycle is.

(a) T3: In practice, T3 cannot be decreased below about 300 K (27ºC), equivalent to a condenser pressure of 0.035 bar. This is because of two tractors:

(i). Condensation of steam needs a bulk supply of cooling water and such a continuous natural supply below the atmospheric temperature of around 15°C is unavailable.
(ii) If the condenser is to be of a rational size and cost, the temperature difference between the condensing steam and the cooling water must be minimum 10°C.

(b) TI: The extreme cycle temperature T1is also limited to near 900 K (627°C) by the strength of the substance available for the extremely stressed parts of the plant, like boiler tubes and turbine blades. This upper limit is known as the metallurgical limit.

(c)Critical Point:

The steam of the Carnot cycle has a tremendous cycle temperature of well beneath this metallurgical limit due to the properties of steam; it is limited to the critical-point temperature of 374°C (647 K). Therefore modern substance cannot be used to their best advantage with this cycle when steam is the functioning fluid. Also, because the saturated steam and water curves converge to the critical point, a plant working on the Carnot cycle with its extreme temperature near the critical-point temperature would have a very large s.s.c., i.e. it would be very big in size and very costly.

(d) Compression Process

Compressing a very wet steam blend would need a compressor of cost and size of comparable with the turbine. It would absorb work comparable with the advanced by the turbine. It would have a short life because of blade corrosion and cavitation problem. These reasons the Carnot cycle is not useful.