Entropy.ppt
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This document is a presentation on entropy that contains sections on the history, concept, definition, expressions, classifications, applications, and conclusions of entropy. It begins with introducing entropy and its origins from Rudolf Clausius in 1854. It then discusses entropy as a measure of disorder and the number of microscopic states a system can be in. The document defines entropy using Boltzmann's constant and covers the classification of entropy including thermodynamic, statistical, and quantum entropy. It concludes that entropy is a measure of disorder that increases over time according to the second law of thermodynamics.
![CONTEN
History
CONCEP
T
DEE
ERL/LU
A/C
INTRODUCTION :The word “entropy” was created by
German physicist “Rudolf Clausius ” in 1854. Rudolf
Clausius (1822 - 1988)The word has a Greek origin, its
first part reminds us of “energy” and the second part is
from “tropes” which means turning point.
HISTORY :Why’s this notion called entropy, anyway?
From the American Heritage Book of English Usage
(1996): “When the American scientist Claude Shannon
found that the mathematical formula of Boltzmann
defined a useful quantity in information theory, he
hesitated to name this newly discovered quantity
entropy because of its philosophical baggage.The
mathematician JohnVon [sic] Neumann encouraged
Shannon to go ahead with the name entropy, however,
since`no one knows what entropy is, so in a debate you
will always have the advantage.’
Rudolf Clausius (1822 - 1988)](https://image.slidesharecdn.com/phy101ppt-190407091945/85/Entropy-ppt-6-320.jpg)
Entropy.ppt
- 4. WELCOME WE ARE NOT JUST ANOTHER BRICK IN THE WALL CONTEN T History CONCEP T DEE ERL/LU A/C 4 PARTPART 3 PART 2 PART 1 KAZI EMAD B.Sc. in CSE ID: 191902025 Slide (4-7) IKHTIAR B.Sc. in CSE ID: 191902022 Slide (8-11) ASMA B.Sc. in CSE ID: 191902027 Slide (12-14) RAIHAN B.Sc. in CSE ID: 1919024 Slide (15-18)
- 5. CONTEN History CONCEP T DEE ERL/LE A/C Introduction/History Concept Definition And Expression Of Entropy Entropy in real life Law of Entropy Unit of Entropy Classification Applications Conclusion
- 6. CONTEN History CONCEP T DEE ERL/LU A/C INTRODUCTION :The word “entropy” was created by German physicist “Rudolf Clausius ” in 1854. Rudolf Clausius (1822 - 1988)The word has a Greek origin, its first part reminds us of “energy” and the second part is from “tropes” which means turning point. HISTORY :Why’s this notion called entropy, anyway? From the American Heritage Book of English Usage (1996): “When the American scientist Claude Shannon found that the mathematical formula of Boltzmann defined a useful quantity in information theory, he hesitated to name this newly discovered quantity entropy because of its philosophical baggage.The mathematician JohnVon [sic] Neumann encouraged Shannon to go ahead with the name entropy, however, since`no one knows what entropy is, so in a debate you will always have the advantage.’ Rudolf Clausius (1822 - 1988)
- 7. CONTEN History CONCEP T DEE ERL/LE A/C What is entropy? The word entropy is sometimes confused with energy. Although they are related quantities, they are distinct. or energy measures the capability of an object or system to do work. on the other hand, is a measure of the "disorder" of a system. What "disorder refers to is really the number of different microscopic states a system can be in, given that the system has a particular fixed composition, volume, energy, pressure, and temperature. By "microscopic states", we mean the exact states of all the molecules making up the system. Entropy = (Boltzmann's constant k) x logarithm of number of possible states = k log(N).
- 8. CONTEN HISTORY CONCEP T DEE ERL/LU A/C CONCEPT The idea of entropy comes from a principle of thermodynamic dealing with energy .It usually refers to idea that everything in the universe eventually moves from order to disorder , and entropy is the measurement of that change. • Physicists use entropy to measure the amount of disorder in a physical system. • In information theory , entropy is the expected value (average) of the information contained in each message received. • It can be considered as the degree of randomness in a message. Entropy :thermodynamic property-- a quantitative measure of disorder Entropy traces out its origin –molecular movement interpretation-Rudolf Clausias in 1850 The concept of entropy -thermodynamic laws(i.e. the 2nd law of thermodynamics) It can be visualised due to the process of expansion, heating, mixing and reaction. Entropy is associated with heat and temperature.
- 9. CONTEN HISTORY DEE DEE ERL/LU A/Legt/ C Definition and expression of entropy Entropy may be defined as the property of a system which measure the degree of disorder or randomness in the system It is a Greek word which means transformation It is denoted by the symbol ‘S’ Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered
- 10. CONTEN HISTORY DEE ERL/LU CLASSIFICATION A/C 1.Entropy is the sum total of entropy due to positional disorder, vibrational disorder and configurational disorder. i.e randomness due to change of state S=sp+st+sc 2.When a system is undergoing change then the entropy change is equal to the heat absorbed by the system divided by the temperature at which change taken place. ΔS = S2 – S1 = ∫ dq / T T ΔS = dq or TdS = dq this is the II law expression. Suppose the process is undergoing change at constant temperature: 3.From I Law we know that ΔE = q – w or dE = dq – dw or dE = dq – PdV At constant temperature ΔE = 0, therefore dq = PdV. From II law we know that dq = TdS , Substituting this in the above we get, Tds = Pdv ΔS = PdV / T, 4.Suppose the process is undergoing change at constant pressure condition then: T ΔS = (q)p - but we know that (q)p = CpdT T ΔS = Cp dT, Or TdS = Cp dT By integration, 1∫2dS = 1∫2 Cp dT /T S2 – S1 = Δ Cp ln (T2 / T1) This is the entropy change of the system at constant pressure condition from room temperature to the reaction temperature.
- 11. CONTEN HISTORY ERL/LU LE/UE CLASSIFICATION Entropy in real life Thus we can say that more disorder = more entropy more order = less entropy
- 12. CONTEN HISTORY CONCEP T DEE LE/UE CLASSIFICATION Law Of Entropy The second law of thermodynamics, “entropy of an isolated system always increases.” Or in other words “The entropy can be created but not destroyed Unit of Entropy The SI unit for Entropy (S) is Joules per Kelvin (J/K). Clausius is also gives the relation between the units i.e. 1 Clausius (Cl) = 1 (cal/°C) = 4.1868 (J/K)
- 13. CONTEN HISTORY CONCEP T DEE CLASSIFICATION TE/SE CLASSIFICATION Thermodynamical entropy Statistical entropy Entropy in classical world Entropy in quantum world
- 14. CONTEN HISTORY CONCEP T DEE TE/SE ECW/EQ W Thermodynamical Entropy Entropy is defined using Clausius inequality 𝛿𝑄 𝑇 ≤ 0 The cyclic integral of 𝛅Q 𝑇 can be viewed as the sum of all these differential amounts of heat transfer divided by the temperature at the boundary. 𝛿𝑄 𝑇 = 0 (for reversible cycle) 𝛿𝑄 𝑇 < 0 (for irreversible cycle) 𝛿𝑄 𝑇 > 0 (for impossible cycle) by defintion: Let’s define a thermodynamic property entropy (S), such that S2-S1= dS = 𝑑𝑄 𝑇 Statistical Entropy In 1877, Ludwig Boltzmann developed a statistical entropy S. this suggest the connection between entropy and thermodynamic probability,. It may be written as: S=F(Ω)=KBlnΩ Where KB= Boltzmann’s constant Ω = thermodynamic probability
- 15. CONTEN HISTORY CONCEP T DEE ECW/EQ W APPLICATIONS Entropy in classical world Claude E. Shannon introduced Shannon’s entropy , used for measuring entropy of a classical system. Thus shannon’s introduced a entropy , i. e. HS= Pilog2 (1/Pi) Where Pi = probability distribution function Entropy in Quantum world Von Neumann entropy is used for measuring entropy of a quantum system. It gauges order in a given quantum system. The entropy of a quantum state was introduced by von Neumann. This entropy of a state P is defined by S(P)= λilog2 ( 1 λi ) Where λi = Eigenvalues of the density matrix
- 16. CONTEN HISTORY CONCEP T DEE APPLICATIONS CONCLUSION APPLICATIONS We use a shannon’s entropy in information theory. Identify an information processing task – data compression, information transmission, teleportation. Quantum Shannon Theory provides General theory of interconvertibility between different types of communications resources: qubits, cbits, ebits, cobits, sbits… It can store information so that at a later time the information can be reconstructed. Entropy as a measure of entanglement.Entropy is a measure of the uncertainty about a quantum system before we make a measurement of its state.
- 17. CONTEN HISTORY CONCEP T DEE CONCLUSION Conclusion Entropy is the thermodynamic property which is the measure of disorder in a system. It can be expresses by ‘S’=q/t The term is coined by Rudolf Clausius. Entropy is mainly associated with heat and temperature. Disorder can be of 3 types- Positional, Vibrational and Configurational Thermobarometric models is an excellent case study when the application of thermodynamic parameters are involve Second law of thermodynamics implies that the entropy of a universe is increasing continously because energy conservation is not 100% efficient. i.e. some heat is always released. Entropy can be zero At absolute 0 (0 K), all atomic motion ceases and disorder in a substance is zero. entropy will always be positive