International Journal of Pure and Applied Mathematics Volume 119 No. 12 2018, 1675-1683 ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu
CONCEPTS OF THERMODYNAMICS
Dr.N.Selvi1, Dr. P.Sugumar2 Associate Professor 1 2 Department of Physics, BIST, BIHER, Bharath University, Chennai. [email protected]
The branch of science called thermodynamics deals with systems that are able to transfer thermal energy into at least one other form of energy (mechanical, electrical, etc.) or into work. The laws of thermodynamics were developed over the years as some of the most fundamental rules which are followed when a thermodynamic system goes through some sort of energy change.
History of Thermodynamics
The history of thermodynamics begins with Otto von Guericke who, in 1650, built the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres[1-6].
Guericke was driven to make a vacuum to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656[7-13], in coordination with English scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume[14-19]. In time, Boyle's Law was formulated, which states that pressure and volume are inversely proportional.
Consequences of the Laws of Thermodynamics
The laws of thermodynamics tend to be fairly easy to state and understand ... so much so that it's easy to underestimate the impact they have[20-25]. Among other things, they put constraints on how energy can be used in the universe. It would be very hard to over-emphasize how significant this concept is[26-32]. The consequences of the laws of thermodynamics touch on almost every aspect of scientific inquiry in some way.
Key Concepts for Understanding the Laws of Thermodynamics
To understand the laws of thermodynamics, it's essential to understand some other thermodynamics concepts that relate to them[33-39].
Thermodynamics Overview - an overview of the basic principles of the field of thermodynamics Heat Energy - a basic definition of heat energy
Temperature - a basic definition of temperature Introduction to Heat Transfer - an explanation of various heat transfer methods.
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Thermodynamic Processes - the laws of thermodynamics mostly apply to thermodynamic processes, when a thermodynamic system goes through some sort of energetic transfer.
Development of the Laws of Thermodynamics
The study of heat as a distinct form of energy began in approximately 1798 when Sir Benjamin Thompson (also known as Count Rumford), a British military engineer, noticed that heat could be generated in proportion to the amount of work done ... a fundamental concept which would ultimately become a consequence of the first law of thermodynamics[40-45].
French physicist Sadi Carnot first formulated a basic principle of thermodynamics in 1824. The principles which Carnot used to define his Carnot cycle heat engine would ultimately translate into the second law of thermodynamics by the German physicist Rudolf Clausius, who is also frequently credited with the formulation of the first law of thermodynamics.
Part of the reason for the rapid development of thermodynamics in the nineteenth century was the need to develop efficient steam engines during the industrial revolution.
Kinetic Theory & the Laws of Thermodynamics
The laws of thermodynamics do not particularly concern themselves with the specific how and why of heat transfer, which makes sense for laws that were formulated before atomic theory was fully adopted. They deal with the sum total of energy and heat transitions within a system and do not take into account the specific nature of heat transference on the atomic or molecular level.
The Zeroeth Law of Thermodynamics
Zeroeth Law of Thermodynamics: Two systems in thermal equilibrium with a third system are in thermal equilibrium to each other.
This zeroeth law is sort of a transitive property of thermal equilibrium. The transitive property of mathematics says that if A = B and B = C, then A = C. The same is true of thermodynamic systems that are in thermal equilibrium.
One consequence of the zeroeth law is the idea that measuring temperature has any meaning whatsoever. In order to measure a temperature, thermal equilibrium much be reached between the thermometer as a whole, the mercury inside the thermometer, and the substance being measured. This, in turn, results in being able to accurately tell what the temperature of the substance is.
This law was understood without being explicitly stated through much of the history of thermodynamics study, and it was only realized that it was a law in its own right at the beginning of the 20th century. It was British physicist Ralph H. Fowler who first coined the term "zeroeth law," based on a belief that it was more fundamental even than the other laws.
The First Law of Thermodynamics
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First Law of Thermodynamics: The change in a system's internal energy is equal to the difference between heat added to the system from its surroundings and work done by the system on its surroundings.
Though this may sound complex, it's really a very simple idea. If you add heat to a system, there are only two things that can be done -- change the internal energy of the system or cause the system to do work (or, of course, some combination of the two). All of the heat energy must go into doing these things.
Mathematical Representation of the First Law
Physicists typically use uniform conventions for representing the quantities in the first law of thermodynamics. They are:
U1 (or Ui) = initial internal energy at the start of the process
U2 (or Uf) = final internal energy at the end of the process delta-U = U2 - U1 = Change in internal energy (used in cases where the specifics of beginning and ending internal energies are irrelevant) Q = heat transferred into (Q > 0) or out of (Q < 0) the system W = work performed by the system (W > 0) or on the system (W < 0).
This yields a mathematical representation of the first law which proves very useful and can be rewritten in a couple of useful ways:
U2 - U1 = delta-U = Q - W
Q = delta-U + W
The analysis of a thermodynamic process, at least within a physics classroom situation, generally involves analyzing a situation where one of these quantities is either 0 or at least controllable in a reasonable manner. For example, in an adiabatic process, the heat transfer (Q) is equal to 0 while in an isochoric process the work (W) is equal to 0.
The First Law & Conservation of Energy
The first law of thermodynamics is seen by many as the foundation of the concept of conservation of energy. It basically says that the energy that goes into a system cannot be lost along the way, but has to be used to do something ... in this case, either change internal energy or perform work.
Taken in this view, the first law of thermodynamics is one of the most far-reaching scientific concepts ever discovered.
The Second Law of Thermodynamics
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Second Law of Thermodynamics: It is impossible for a process to have as its sole result the transfer of heat from a cooler body to a hotter one.
The second law of thermodynamics is formulated in many ways, as will be addressed shortly, but is basically a law which - unlike most other laws in physics - deals not with how to do something, but rather deals entirely with placing a restriction on what can be done.
It is a law that says nature constrains us from getting certain kinds of outcomes without putting a lot of work into it, and as such is also closely tied to the concept of the conservation of energy, much as the first law of thermodynamics is.
In practical applications, this law means that any heat engine or similar device based on the principles of thermodynamics cannot, even in theory, be 100% efficient.
This principle was first illuminated by the French physicist and engineer Sadi Carnot, as he developed his Carnot cycle engine in 1824, and was later formalized as a law of thermodynamics by German physicist Rudolf Clausius.
Entropy and the Second Law of Thermodynamics
The second law of thermodynamics is perhaps the most popular outside of the realm of physics because it is closely related to the concept of entropy or the disorder created during a thermodynamic process. Reformulated as a statement regarding entropy, the second law reads:
In any closed system, the entropy of the system will either remain constant or increase.
In other words, each time a system goes through a thermodynamic process, the system can never completely return to precisely the same state it was in before. This is one definition used for the arrow of time since entropy of the universe will always increase over time according to the second law of thermodynamics.
Other Second Law Formulations
A cyclic transformation whose only final result is to transform heat extracted from a source which is at the same temperature throughout into work is impossible. - Scottish physicist William Thompson (Lord Kelvin)
A cyclic transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible. - German physicist Rudolf Clausius
All the above formulations of the Second Law of Thermodynamics are equivalent statements of the same fundamental principle.
The Third Law of Thermodynamics
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The third law of thermodynamics is essentially a statement about the ability to create an absolute temperature scale, for which absolute zero is the point at which the internal energy of a solid is precisely 0.
Various sources show the following three potential formulations of the third law of thermodynamics:
1. It is impossible to reduce any system to absolute zero in a finite series of operations. 2. The entropy of a perfect crystal of an element in its most stable form tends to zero as the temperature approaches absolute zero. 3. As temperature approaches absolute zero, the entropy of a system approaches a constant
What the Third Law Means
The third law means a few things, and again all of these formulations result in the same outcome depending upon how much you take into account:
Formulation 3 contains the least restraints, merely stating that entropy goes to a constant. In fact, this constant is zero entropy (as stated in formulation 2). However, due to quantum constraints on any physical system, it will collapse into its lowest quantum state but never be able to perfectly reduce to 0 entropy, therefore it is impossible to reduce a physical system to absolute zero in a finite number of steps (which yields us formulation 1).
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