Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.The thermodynamic concept was referred to by Scottish scientist and engineer Macquorn Rankine in 1850 with the names thermodynamic function and heat-potential. In 1865, German physicist Rudolph Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature. He initially described it as transformation-content, in German Verwandlungsinhalt, and later coined the term entropy from a Greek word for transformation. Referring to microscopic constitution and structure, in 1862, Clausius interpreted the concept as meaning disgregation.A consequence of entropy is that certain processes are irreversible or impossible, aside from the requirement of not violating the conservation of energy, the latter being expressed in the first law of thermodynamics. Entropy is central to the second law of thermodynamics, which states that the entropy of isolated systems left to spontaneous evolution cannot decrease with time, as they always arrive at a state of thermodynamic equilibrium, where the entropy is highest.
Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics, and found the link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behavior, in form of a simple logarithmic law, with a proportionality constant, the Boltzmann constant, that has become one of the defining universal constants for the modern International System of Units (SI).
In 1948, Bell Labs scientist Claude Shannon developed similar statistical concepts of measuring microscopic uncertainty and multiplicity to the problem of random losses of information in telecommunication signals. Upon John von Neumann's suggestion, Shannon named this entity of missing information in analogous manner to its use in statistical mechanics as entropy, and gave birth to the field of information theory. This description has been proposed as a universal definition of the concept of entropy.
There is a fascinating demo on YouTube of "32 metronomes synchronizing". They are all started at different times but in barely more than 2 minutes they are all synchronized and working as one unit. If you have not seen this then go to Google and type in "metronomes synchronizing".
Could somebody...
Can we always express the entropy of a given system as ##\partial U / \partial T##, i.e. as the variation of the internal energy of the system w.r.t. its temperature?
By always I really mean, in every discussion we are eventually engaged in. Like, when I want to talk about the evolution of the...
Our universe is considered a closed system. Law says that the entropy of a closed system is bound to increase.
Then how could living beings evolve when they are an extremely ordered system?
From what I have heard, entropy is the amount of energy that is unavailable to do work. What exactly does it mean by "unavailable energy", and can someone give some examples of energy being unavailable to do work in real life?
Homework Statement
The fundamental equation of a system of \tidle{N} atoms each of which can exist an atomic state with energy e_u or in atomic state e_d (and in no other state) is
F= - \tilde{N} k_B T \log ( e^{-\beta e_u} + e^{-\beta e_d} )
Here k_B is Boltzmann's constant \beta = 1/k_BT...
Homework Statement
Water vapor at 6 MPa, 600C enters a turbine operating at steady state and expands to 10 kPa. The mass flow rate is 2 kg/s, and the power developed is 2626 kW. Stray heat transfer and kinetic and potential energy effects are negligible. Determine (a) the isentropic turbine...
In classical mechanics, if a system consisting of one particle suddenly became two particles, the entropy of the system would increase because the number of spatial degrees of freedom would double. But, in QM, I believe, when one particle decays into two particles, the two new particles would be...
it seems it is not reasonable
Sorry
it said that delta S>=0
in an isolated system. i know why they put " = " sign, but i don't know why it is still possible that dS>0 in an isolated systembecause in an isolated system,it is said that dQ=0 (because no heat transfer between the system and the...
Homework Statement
This is a state ecuation of a gas:
PV=AT+B/V, where A and B there are constants.
First: Demonstrate that ##c_V## depends only of T
Second: Find U(T,V) and S(T,V)
Homework Equations
##\left(\frac{\partial U}{\partial S}\right)_V=T\text{ (1)}##
##\left(\frac{\partial...
Why do they introduce the partition function. I have seen it in the derivation of the Boltzmann distribution. But I don't know the physical significance of it here? And how do they get to (L.11) after that? I get everything until L.7. Including L.7.
The rest of the proof is here just in case...
I know that early oscillating models of the universe fail due to the second law of thermodynamics. One thing that I am unclear about is since as far as i know the laws of physics break down in a singularity can the second law of thermodynamics break down also?
When I see comments to the...
Dear community,
I stumbled upon this ecology article (https://www.witpress.com/elibrary/dne/4/2/402, page 4) and have some confusion about a statement in there:
"Before further unpacking the formal defnition of entropy, one would be justifed in asking why not simply choose (1 – p) instead of...
Hi everyone!
1. Homework Statement
Given is a function for the internal energy: ##U(T,V)=Vu(T)##
Asked is to derive the entropy balance equation. In order to do so i need to find the "isothermal and adiabatic compressibility": $$\kappa_{T}=-\frac{1}{V}\left(\frac{\partial V}{\partial...
In order to better explain my question let me give a precise situation and then state my question
Say I have a well insulated rigid container containing some mass m of a saturated liquid-vapor mixture of water at some pressure P1. Initially it's at some quality x1. An electric resistance heater...
Homework Statement
A 5.0-kg piece of lead at a temperature of is 600 Celsius placed in a lake whose temperature is 15 Celsius. Determine the entropy change of (a) the lead piece, (b) the lake, and (c) the universe.
mass of lead=5 kg
initial temperature of lead=873.15 K
final temperature of...
Entropy is often represented as a representation of disorder in a system or the amount of energy deposited as unusable in a system. What are the other perspectives about entropy?
Something I've always wondered: why do we measure the amount of disorder (entropy) rather than the amount of order?
We don't measure brightness by the amount of "dark". Surely order is the thing of interest, so why don't we measure that rather than measuring the absence of it?
And in...
Hello, I am a curious layman, so I might have some misconceptions. I have been pondering some questions, and I was hoping someone might be able to either confirm, or explain this. What I am wondering, if I am understanding this correctly, is why atoms do not experience entropy? If this is true...
Hi.
I found following exercise in a high school textbook:
"Compute the entropy change in following process:"
The solution is
"The number of particles decreases from ##N_1## to ##N_2=N_1/2##. Hence the entropy decreases by
$$\Delta S=-k\cdot N_1\cdot \ln{2}\enspace ."$$
I can't quite follow...
Hi. This is the problem 5.1-1 from the second edition of Callen's Thermodynamics. It says
Formulate a proof that the energy minimum principle implies the entropy maximum principle. That is, show that if the entropy were not maximum at constant energy then the enrgy could not be minimum at...
The Theory. Newton's Third Law of 1)Motion states: 'To every action there is an equal and opposite reaction'. ... The force exerted by the second body on the first body is called reaction. The action and reaction are equal and opposite.
2)Second Law of Thermodynamics : In any cyclic process the...
Why is it so much easier to increase the temperature of something than it is to decrease the temperature?
Why are refrigerators more complex than stoves?
I began reading Mehran Kardar's Statistical Physics of Particles and about halfway through the first chapter, there was a discussion on the second law of thermodynamics. He makes no mention of the old tenet that 'the total entropy in the universe must always increase' (I'll refer to this as the...
Is there something like ##\frac {dS\dt}=...## Like in the general system,
I know its always positive but I want to know is there any constant quantity of the universe like universe entropy increases amount of 45J/C or something like that.Or it depends only the knows closed systems which we ca...
I've been reading some speculative articles about the possible quantum arrow of time which emerges through collapse and irreversibility.
My question is: does collapse in the Copenhagen interpretation (or perhaps in a objective-collapse model) allow the spontaneous decrease of entropy where an...
Homework Statement
5 moles of liquid argon undergoes vaporization at its normal boiling point (87.5 K) and the resulting argon gas is subsequently heated to 150 K under constant volume conditions. Calculate the change of entropy for this process. The standard enthalpy change of vaporization, ∆...
1-Whats the relationship between entropy and İnformation ?
2-Can Entrophy always increases statement imply information lost ?
3-If it implies how its lost ?
Consider an expanding universe of infinite extent containing only a single particle. Does the entropy of this universe increase over time due to expansion? If it makes any difference in being a sensible question, consider an expanding universe with N particles where N is a known, finite number.
Calculate the change in entropy for the system, the surroundings and the Universe if 2 moles of ethane are completely combusted at 298 K. Standard entropies of C2H5(g), O2(g), H2O(l) and CO2(g) are 229.6, 205.1, 69.9, 213.7 J mol-1 K-1 , respectively. Standard enthalpy changes of formation of...
Hi.
I just read an article where following cooling method is described. Apparently it's very common, but I don't know what it's called:
A gas under pressure is released into a vacuum through a small hole. The average particle speed in this beam of gas is the same as before, but the...
Hello.I have a question about entropy of a thermodynamic system.
1)If we have let say a gas that is separated by some thermo isolated walls (so no heat goes in or out) does the entropy of that gas conserve? I taught that if S=dQ/dt, because Q=0,then the entropy should be conserved.
2)So,does the...
Consider the dependence of entropy and of temperature on the reduced Planck's constant (taken from page 23 of Thomas Hartman's lecture notes(http://www.hartmanhep.net/topics2015/) on Quantum Gravity):
$$S \propto \hbar, \qquad \qquad T \propto \hbar.$$
I do not quite see how entropy can depend...
Homework Statement
There exists a tank filled with air with a given volume, temperature, and pressure. The tank exists in a room at a given temperature and pressure.
That is:
For the tank: P=1MPa, T=700k, V=1m^3
Outside: T=295K, P=100kPa
Homework Equations
\psi 2-\psi...
Hi. This is the problem I'm trying to solve:
A system may be in two quantum states with energies '0' and 'e'. The states' degenerescences are g1 and g2, respectively. Find the entropy S as a function of the Energy E in the limit where the number of particles N is very large. Analyse this...
MENTOR NOTE: NO TEMPLATE BECAUSE SUMITTED TO WRONG FORUM.
3.1) A quantity of 0.10 mol of an ideal gas A initially at 22.2 degrees C is expanded from 0.200 dm3 to 2.42 dm3 . Calculate the values of work (w), heat (q), internal energy change (delta U), entropy change of the system (deltaSsys)...
Homework Statement
A hot rock ejected from a volcano's lava fountain cools from 1100º C to 40.0º C and its entropy decreases by 950 J/K. How much heat transfer occurs from the rock? (Source: OpenStax "College Physics for AP Students", Chapter 15.6)
Homework Equations
I used the equation ΔSh +...
The second law of thermodynamics predicts the end of the life of the universe being one where thermal equilibrium exists throughout the universe (maximum entropy) - essentially all energy has been dissipated. My question is if according to the first law of thermodynamics which describes the...
Homework Statement
For some reason it is not letting me add the image here, here is the link to the question:
http://imgur.com/a/3DLWM
The part I'm stuck on is the last part. Basically, the question is to obtain the following equation for the entropy of vaporisation using the Redlich-Kwong...
https://en.wikipedia.org/wiki/Future_of_an_expanding_universe "Over an infinite time there could be a spontaneous entropy decrease, by a Poincaré recurrence or through thermal fluctuations (see also fluctuation theorem)"
Homework Statement
5 kg of water at 60 degrees are put in contact with 1 kg of ice at 0 degrees and are thermally isolated from everything else. The latent heat of ice is 3.3x105 J/kg.
What is the change of entropy of the universe when 100J of energy are transferred from the water to the ice...
Homework Statement
A well-insulated tank of volume 6 m3 is divided into two equal volumes. The left part is initially filled with air at 100 C and 2 bar, and right side cell is initially empty. A valve connecting two cells will be opened so that gas will slowly pass from cell 1 to cell 2. The...
Homework Statement
It is problem 21 in the attached file.
Homework EquationsThe Attempt at a Solution
The answer seems to be C. I thought it is D. Can someone explain it to me please?
Sorry if this is a stupid question, I don't fully understand entropy. Snow flakes are highly structured, they form from water vapor which has very little structure. I must be misunderstanding entropy, my interpretation of it is that isolated system must evolve into more chaotic less structured...
In holographic entanglement entropy notes like here, they let alpha go to one in (2.41) and get (2.42). But (2.41) goes towards infinity, when doing that! Can someone explain how alpha --> 1 will make (2.41) into (2.42)? Thank you!
Hello.
The entropy S is a state variable or state function as the integral of dS = dQ/T is a path-independent, provided that the path is reversible process path. However, such a path-independency of the integral breaks down when the path includes irreversible process. So, I guess we can only...