Tagged Questions

A important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

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What is the physical implication of Clausius inequality?

Clausius inequality is given as: $$\oint \frac{\delta Q_\text{res}}{T_\text{res}} \le 0\;.$$ From Carnot cycle, we get the equality relation as the entropy lost by the hot reservoir is the same as ...
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Why does slow compression of a gas doesn't change its entropy to increase?

This is quoted from Daniel V Schroeder's Thermal Physics: It's interesting to think about why the slow compression of a gas doesn't change its entropy to increase. One way to think about it is to ...
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What is the cause for the inclusion of 'thermal equilibrium' in the statement of Ergodic hypothesis?

This is the fundamental assumption of statistical mechanics: In an isolated system in thermal equilibrium $^1$, all accessible microstates are equally probable. But why does it mention the ...
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Why is there no change in internal energy for an isothermal reversible process?

This concept is used for deriving the relation : Change in Entropy = $2.303 \,\ nR \,\ log_{10} (\frac{V_2}{V_1})$ But I don't understand why change in Internal energy = $0$.
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Why doesn't entropy get decreased in adiabatic expansion process?

I was reading the second step of Carnot cycle in which the system undergoes adiabatic expansion doing work & thus decreasing the internal energy of itself. The entropy didn't change as no further ...
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How does the second law of thermodynamics forbid the possibility of perpetual machine of the second kind?

Fermi in his lecture asserts: The second law of thermodynamics rules out the possibility of constructing a perpetuum mobile of the second kind. So, this means there can be no machine which just ...
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Why does heat added to a system cause an increase in entropy that is independent of the amount of particles in the system?

Say we have two gas containers of $N_{2}$ at the same temperature of $300 ~\text{K}$, one containing $10^{23}$ particles and the other containing $10^{13}$ particles. If we add a quantity of heat to ...
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Change in statistical Entropy negative?

I'm currently stuck with a particular problem: The total energy of a set of molecules in an "isolated" container does not change when the container volume expands by a factor of 2, ...
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Thermodynamics - Entropy Change in an Isolated System and the State Postulate

I was thinking about something. Consider a isolated system consisting of hot and cold water in a rigid tank. The process is to basically to let them reach an equilibrium temperature. Now, because it's ...
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Why is the change in entropy greater for processes occurring at lower temperatures? [duplicate]

We have the thermodynamic definition of entropy $\Delta S = q_{rev}/T$. If heat transfer is the same for both processes at different temperatures, this implies that the same process occurring at lower ...
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Le Chatelier's principle and energy minimization

In Callen's "Thermodynamics" in section 8.5 he asks us to imagine some perturbation $dX$ of an extensive parameter of a system in contact with a reservoir that acts to hold fixed the intensive ...
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Is it possible that my 750ml water bottle contains spent fuel from a space shuttle launch

Firstly I live in New Zealand which is very distant from USA which is where the space shuttle was originally launched from. So what is the possibility of molecules from the rocket engines spent ...
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How is one process reversible and its reverse non-reversible?

My textbook gives this example of a reversible process: A gas in a piston is expanded over a long period of time, sitting on a hot plate that maintains its temperature. As an infinitesimal amount of ...
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Light Sheets and the Holographic Entropy Bound

I'm trying to understand light sheets as related to the holographic entropy bound for information. This bound equates the information on a surface (e.g. the event horizon of a black hole) with the ...
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Why is the second law of thermodynamics indisputable? [duplicate]

Why is the second law of thermodynamics undisputable? On his website Professor Hawking says the following: The cosmologist, Sir Arthur Eddington, once said, 'Don't worry if your theory doesn't ...
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How is the efficiency of a heat engine related to the entropy produced during the process?

I'm reading Schroeder's An Introduction to Thermal Physics. Regarding heat engines, it is stated: Unfortunately, only part of the energy absorbed as heat can be converted to work by a heat engine. ...
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Best introduction to the link between information and thermodynamics

I have a solid understanding of classical thermodynamics, as well as a reasonable understanding of statistical mechanics and some of the philosophical issues regarding entropy. However, I've never ...
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Mach Number after Normal Shock

Is there any way that someone can give me more of a conceptual explanation for the fact that the Mach number downstream of a normal shock must be less than or equal to 1? I understand the ...
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Derive the Boltzmann factor in classical statistical mechanics

In both quantum and classical statistical mechanics, the probability of an NVT system having an energy $E$ is proportional to $$p(E)\propto e^{-E/T}$$ However, all of the derivations (that I can ...
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Are the fundamental forces constantly fighting entropy?

If we imagine that the four fundamental forces disappeared, all structures that had a non zero temperature (Kelvin) would quickly disintegrate due to the particles colliding with each other and start ...
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Did the early universe violate the 2nd law of thermodynamics? [duplicate]

If the universe started out isotropic and homogenous and of all fundamental particles then how could there now be any concentration of energy anywhere? If you say that nothing is really homogenous ...
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Is entropy violated inside black holes and worm holes?

Do the laws of thermodynamics hold true everywhere in universe ? What about black holes and worm holes ?
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The statistical interpretation of Entropy

I recently got introduced to the Statistical Mechanics, particularly, the Statistical Interpretation of Entropy and am utterly confused regarding the following problem: Imagine a box with two ...
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difference between reversible and irreversible entropy

Before I proceed, let me first say I have done research and understand the general idea between the two: summed up crudely reversible happens in a slower continuous manner while irreversible happens ...
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Understanding entropy [duplicate]

I am currently doing some research on entropy and I am trying to get my head around the concept. One thing that I am getting right now is that entropy is just an application of probability and ...
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sudden volume increase piston

I am wondering what happens in the following situation. I have a piston filled with an ideal gas for which I suddenly/instantaneaouly iscrease the volume. In particular I want to know what happens to ...
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If Hawking radiation is proved to be true won't black holes lose entropy which is against laws of thermodynamics?

Hawking radiation states that black holes continuously emit radiation. But if its the case won't entropy of black holes decrease which violates the laws of heat, entropy and thermodynamics?
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Facing a difficulty in calculating thermal entropy of a massless scalar field in a d-dimensional box at temperature T

I try to calculate the thermal entropy of a massless scalar field in a box at finite temperature T. The calculation is almost mindless but I meet a math problem that I don't know how to solve. My ...
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Do the entropy of the universe and third law of thermodynamics conflict? [duplicate]

We know that our universe was in low entropy state at the earlier time after the Big bang. But we also know that the temperature at that times was enormously high. But what the third law of ...
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Entropy definitions

So I have learned that entropy is the measure of disorder of a system. For the IPhO this was of course not enough as we need to be able to calculate entropy changes of ideal gases. Those equations ...
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Where is the flaw in this machine that decreases the entropy of a closed system?

I was thinking about a completely unrelated problem (Quantum Field Theory Peskin & Schroeder kind of unrelated!) when the diagram below sprang into my mind for no apparent reason. After some ...
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Why is the entropy of most systems not infinite?

We can define a microstates as follows: Definition 1: A complete specification of the six coordinates of each molecule of a system, within the limits of the dimensions of the cell in which its ...
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I recently read in the news that Stephen Hawking claims to have solved the Black Hole Information paradox. I researched a bit about the paradox and the research that Stephen Hawking did to solve it. ...
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Is entropy a meaningful concept on a quantum level?

My naive assumptions, as I really am at a pretty basic stage in QM, are as follows: Classically, entropy gives us a practical measure of the direction of time, as opposed to our physical laws which, ...
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Why don't photons split up into multiple lower energy versions of themselves?

A photon could spontaneously split up into two or more versions of itself and all the conservation laws I'm aware of would not be violated by this process. (I think.) I've given this some thought, and ...
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Entropy reversal in magnets

Entropy is an irreversible phenomenon without any energy supplied to reverse it. I was reading about paramagnetic substances and how dipoles align inside them on application of magnetic field. My ...
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If heat can't be transformed into other forms of entropy, why do hot things radiate electromagnetic waves?

The laws of entropy says entropy can only increase. On the other hand, if I take a hot object, it will naturally convert its heat into EM radiation. How is this possible? Does EM radiation count as ...
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What is the relationship between entropy and work? [closed]

Can someone explain the relationship between entropy and work? I've been reading my textbook and looking online but I feel like I'm missing something. Can someone explain it in layman's terms :)
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Luminosity and entropy of a relativistic shell

I am looking to understand more about gamma ray bursts. The review I am reading through describes in equations (111), (112) the luminosity of a relativistic plasma shell, in an inertial frame at rest ...
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Exploding planets and entropy

Say we have a planet and we blow it up to tiny pieces that gets spread out in a cloud of debris around the planets original location. This cloud of debris is analogue to a cloud of water wapor in ...