• rameez badhurshah

Carnot Engine Cycle

Engine - The heart of every vehicle, but how does the engine work to propel the vehicle? Can the engine work with 100% efficiency? What are the laws that govern the fundamentals of heat engines or heat pumps?


Table of Contents

  1. Introduction

  2. Laws of thermodynamics

  3. Entropy a. Principle of increase in entropy

  4. Reversible engine cycle (Carnot cycle) a. Carnot Theorem

  5. Summary

Before we start, let us understand the importance of learning the heat engine. Almost all the vehicles that use petroleum products as their working fluid, work on one of the heat engine cycles. Based on the necessity, one can choose a different cycle, for example, a truck works on the Diesel cycle whereas a car mostly works on the Otto cycle. But these cycles have low efficiency. Let us understand why an engine cycle namely the Carnot cycle having the maximum efficiency can only be an ideal theoretical cycle and never be practically achievable. Also, why this cycle frames the basis for comparison of other cycles. We discussed a lot of processes in the last post, yet we will be discussing an additional very important process, namely the isentropic process here.

Although electric vehicles are now gaining popularity, these cycles drove the automotive industry for more than one and a half-century (160 years). So, let us drive into the fundamentals and understand the working of these cycles.

 

Laws of Thermodynamics.

Some fundamental laws govern the science of thermodynamics. These laws have evolved over time. A heat engine is a direct application of the second law of thermodynamics. But besides this law, there are other three laws. At this point, it would be a great addition to the topic to state these laws here

First law of Thermodynamics :

"The algebraic sum of heat transfer in a cyclic process is directly proportional to the algebraic sum of work transfer in that cyclic process."

Simply put, the first law is nothing but the law of conservation of energy - "Energy can neither be created nor be destroyed. It can only be converted from one form to another. The total amount of energy in the universe always remains constant." Thus, the total heat energy in a cyclic process will be equal to the total work done. Although the law is fundamental in nature, it has certain following limitations:

  1. It cannot identify the direction of energy transfer

  2. The quantitative analysis of the conversion of heat to work cannot be calculated

  3. Also, the qualitative analysis of energy cannot be determined.

Second law of Thermodynamics :

For the second law, there are two popular statements given independently. Let's first have both the statements and then we can see the similarity in both the statements.

Kelvin-Planck Statement: "There cannot be a device which works on the cyclic process to produce the sole effect of work from the given quantity of heat supplied to it."

Claussius Statement: "It is impossible to construct a cyclic device to transfer heat from a low temperature to a high-temperature body without any external assistance."

Following are some of the important observations which make understanding these statements easier.

  1. Work done will never be equal to heat supplied. Work output will always be less than the heat supply

  2. Efficiency defined as work done by heat supply will never be 100%.

  3. For any heat engine or heat pump to operate, it requires a source and sink. The source is a heat reservoir capable of supplying heat at a constant temperature while the sink is a heat reservoir that is capable of receiving heat at a constant temperature.

  4. There can be multiple heat reservoirs but, at least one of them should be a source and a sink

Since we have exclusively discussed heat engines and heat pumps above. A heat pump is not necessarily a refrigerator. Let us distinguish between them.


Heat Engine: It is a device to convert thermal energy to mechanical energy

Heat Pump: It is a device to transfer heat and maintain high-temperature space in the surrounding which is at low temperature with help of internal energy


Refrigerator: It is a device to transfer heat from space and to maintain that space at low temperature in the high temperature surrounding with help of external energy.


Zeroth law of Thermodynamics :

The zeroth law was more fundamental but was given after the first and the second laws, hence instead of naming it as the third law of thermodynamics, the name was given as zeroth law of thermodynamic. The statement is as follows :

"When two bodies are in thermal equilibrium individually with the third body, then all three bodies must be in thermal equilibrium amongst themselves."



The importance of zeroth law is that it is a fundamental law on which the temperature of different bodies is measured. This principle is used to measure the temperature of anybody or calibrate thermometers and temperature sensing devices.


Third law of Thermodynamics :

The third law deals with the entropy of the system and the statement is given as "The entropy of a perfect crystal of a pure substance approaches zero as the temperature approaches zero."

Here, we will first try to understand the concept of entropy. Once entropy is well understood, the law becomes self-explanatory.

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Entropy

Entropy is a very interesting concept in classical thermodynamics as well as statistical mechanics. In fact, the very concept of entropy amazed Christopher Nolan and he used this in his sci-fi movie Tenet. Entropy is simply the amount of disturbance or more accurately disorderliness in the system. Mathematically, for a reversible process, the change in entropy is defined as :

Entropy change can also be defined as a measure of irreversibility associated with the process. Entropy change does not depend on the path between the end states, hence entropy is a point function. Combining the fundamentals of the first and second law of thermodynamics, the entropy change for various processes can be further expressed as

Isentropic process: A process in which the entropic remains constant. The only way to isentropic process is having a reversible adiabatic process. Two isentropic processes can never intersect each other. This is an idealistic process as all the real processes are irreversible in nature.

Principle of increase in entropy:

The entropy change of the universe always increases. Only for a reversible process, the change of entropy may remain constant. The more molecular motion and interaction, the greater is the entropy. Thus, the gases have a higher entropy as compared to liquids. Solids have the least entropy. To achieve constant entropy, the following conditions need to be achieved for the process to be reversible

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Conditions for reversibility

  1. The process should be infinitesimally slow

  2. Heat transfer should take place within an infinitesimal temperature difference.

  3. There should not be any free expansion

  4. There should not be any dissipative forces like mechanical friction or fluid friction.

Now that we are well versed with the concept of entropy as well as the isentropic process, let us finally get versed with the Carnot engine cycle or the reversible engine cycle.

 

Reversible engine cycle or Carnot cycle

French thermodynamics Sadi Carnot proposed a theoretical thermodynamic cycle, namely the Carnot cycle. The pressure-velocity diagram or more commonly known as the PV diagram for the Carnot engine cycle is shown above. The cycle is ideal and mainly provides the maximum efficiency that a heat engine cycle can produce. The cycle consists of 4 processes given as below.

  1. Process 1-2 - Isothermal Expansion: The first process is the heat addition (Q1) process which takes place at a constant temperature.

  2. Process 2-3 - Adiabatic Expansion: The process is also called isentropic expansion, thus the heat transfer in this process is zero and the work output by the system on the surrounding takes place here

  3. Process 3-4 - Isothermal Compression: The next process involves compression at a constant temperature with the release of heat (Q2)

  4. Process 4-1 - Adiabatic Compression: The final process involves work done on the system by the surrounding with no heat supply.

Efficiency

The efficiency of such a system can be expressed in the below form.

where 'W' is the work done, 'Qs' is the heat supplied, 'Qr' is the heat released, 'Tmin' is the lower temperature limit while 'Tmax' is the upper-temperature limit. Thus, we observe, the efficiency here is majorly dependent on the two temperatures the cycle operates on, namely the minimum and the maximum temperature. The larger the difference between the two temperature ranges, the higher is the efficiency. The efficiency of 100% can never be practically achieved since the lowest temperature can never reach 0 kelvin. Another interesting observation here is that the efficiency does not depend on the working substance. One direct consequence of the Carnot cycle is the Carnot theorem which frames the basis for the comparison of the efficiency of any other cycle.

Carnot Theorem:

Amongst all the heat engines working between the same temperature limits, the reversible heat engine (Carnot engine) is the most efficient. However, the Carnot cycle is not an ideal cycle.

Reasons why the Carnot cycle is not suitable as an ideal cycle.

  1. Carnot cycle is made of reversible processes, which are only ideal. All real processes are irreversible in nature.

  2. The cycle is made of adiabatic and isothermal processes which are expected to be very fast and very slow process respectively. It is practically impossible to incorporate the same in the same cycle.

  3. The swept volume of the Carnot cycle for a given purpose is many times higher than other cycles.

  4. The mean effective pressure (m.e.p.) of the Carnot cycle is much lower compared to other cycles. Here, m.e.p. indicates the ability of power produced. Hence, for the same power produced, it becomes more voluminous and complicated.

History

Although the works on principles of thermodynamics were already in place, the first and second laws of thermodynamics were only framed as a statement much later 1850s. These laws were based on works of great thermodynamicst like William Rankine, Rudolph Clausius, and Lord Kelvin. The zeroth law was given only in the year 1931 by R.H Fowler. Being fundamental, the law was labelled as zeroth law and not as third law. Whereas during the years 1906–12, the third law emerged from works by chemist Walther Nernst. Entropy in Greek means a turning point and was indeed coined smartly by Rudolph Clausius which indeed turned out as turning point in thermodynamics

Summary

  • We discuss the fundamental laws of thermodynamics

  • Understanding of a very important concept - Entropy and the process related with constant entropy

  • Finally, we discuss the Carnot cycle in detail, the conditions required for the cycle to operate and why even such an efficient cycle is only true on paper and cannot be considered as an ideal cycle.

Thermodynamics and energy is a fun thing to learn. It's behavior, characteristics and applications are wide and is essential in many way than we know. To know more about interesting concepts in Thermodynamics, subscribe to our page!


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