Tagged Questions

A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work

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Entropy of this system

We have a system with two energy states $E_0$< $E_1=0$. We also know that state $E_0$ can only take at most $m$ particles. Curently, there are $n<m$ particles in $E_0$. Now, I am supposed to ...
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1answer
30 views

Entropy change at varying volumes

I have two questions both related to each other: 1.What is the effect of change in volume (whether increasing or decreasing), of a system, under isothermal conditions? How does this change in ...
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41 views

Can any one solve this integral equation? [on hold]

I am presently working in the area "entanglement entropy". When i am trying to solve the integral equation $$\int_{-\infty}^{+\infty} dx_2' \rho_{2}(x_2, x_2') f_n(x_2') = p_n f_n(x_2)$$ for ...
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1answer
56 views

Why doesn't a Brownian ratchet provide free energy?

A Brownian ratchet is described here at Wikipedia. The "why it fails" section reads: Feynman demonstrated that if the entire device is at the same temperature, the ratchet will not rotate ...
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1answer
54 views

Imaginary time is to inverse temperature what imaginary entropy is to …?

The Wick-Rotation rotates imaginary time into inverse temperature (as can be seen from its "rotating" the Schrödinger equation into the heat equation). Now since entropy is temperature's conjugate, I ...
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Does entropy increases due to gravity? [closed]

Imagine travelling to the surface of a neutron star where the very intense gravity would make you weigh 140 trillion times more than we do on earth. It's enough to significantly raise the entropy of ...
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2answers
111 views

Why can we say that $\bar{d}Q=TdS$?

When we introduce entropy we do this by saying that: $$\bar{d}Q=TdS.$$ Now I was wondering why this should be true? I know that by looking at a Carnot cycle, we do get this relation for reversible ...
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1answer
41 views

entropy of a long molecule chain with respect to its length

Consider a (very long) one-dimensional chain of $N$ moleculs, which can be in either of the energy states $\alpha$ or $\beta$. The configurations have length $a$ or $b$ respectively. Show ...
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2answers
56 views

What is the conceptual difference between Gibbs and Boltzmann entropies?

In simple words what is the conceptual difference between Gibbs and Boltzmann entropies? Gibbs entropy: $S=-k_B\sum p_i\ln p_i$ Boltzmann entropy: $S=-k_B\ln \Omega$
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Calculating entropy [duplicate]

Suppose 30 gram of metal Gallium melts at 36 °C. The specific heat of fusion is 80.3 kJ/kg and the melting temperature is 29.9 °C. Explain if the melting of the Gallium in this process is ...
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How much of elastic energy is stored as entropy?

There are two cases of elastic stretching: springs and rubber. When you streach a spring or a piece of rubber both absorb some energy as Entropy (S) and some as plain energy (U) $$\displaystyle{ ...
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38 views

Consequences of Entropy/Information Reversal in a System?

Can pairs of different physical systems be symmetrical under a process which would turn one of these physical system's entropic and informational contents into another system's respective ...
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2answers
150 views

Violation of the second law of thermodynamics? [closed]

Here is a machine which seems to violate the second law of thermodynamics: $A$ and $B$ are point black bodies of the same temperature (initially). everything is rotationally symmetric around the ...
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87 views

Contradiction on Entropy of the “universe” decreasing

I have hit what seems to be a contradiction concerning entropy. In my class, we measured the entropy change of photosynthesis which is obviously a non-spontaneous process. We used the formula, ...
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72 views

Isentropic and Isothermal Compressibility

Why isentropic compressibility is greater than isothermal compressibility ? While deriving $C_p$ and $C_v$ relation, I got $\frac{Cp}{Cv}$ as $\frac{ke}{Kt}$. Which tells us that $Ke > Kt$. But ...
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1answer
38 views

Isentropic process and reversibility [duplicate]

I know that every adiabatic reversible process is an isentropic process. Can a process be isentropic but still not reversible adiabatic? Please provide me some examples.
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1answer
42 views

Unmixing of gases: What is the relevant temperature for my Entropy?

This answer to a question about unmixing gases states: However, let us now assume we have to hand a source of mechanical work, and a large heat reservoir at temperature $T$. I'll assume that ...
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1answer
22 views

How does entropy change when heat is transfer into a system reversibly with constant T?

My guess will be deltaS system : increase [because heat is flowing into the system] deltaS surrounding: decrease [because heat is leaving the environment] deltaS universe (sys+surr) : 0 because it ...
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2answers
41 views

For change in entropy dS = dq/T, is T the temperature of system or surrounding or both?

For change in entropy dS = dqrev/T, is T the temperature of system or surrounding or both? I am confused about Thot, Tcold, Tsys and Tsurr. If qrev, are we talking about the reversible cycle such as ...
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135 views

Does entropy have a physical meaning?

Entropy is incredibly useful as a mathematical tool. But what does it actually mean? I understand that the Boltzmann entropy is defined by: $$S=k\ln{\Omega}$$ With $\Omega$ being the multiplicity ...
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2answers
35 views

Does the relation between entropy and temperature depend on the ensemble?

If we change the temperature of a given system, there will be a relation between its entropy and temperature S(T). Is S(T) the same in a canonical ensemble and a grand canonical ensemble? If not, is ...
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2answers
234 views

Difference between irreversible and entropy?

Cedric Villani recently wrote an article on Landau damping, where at least one topic discussed confused me. Besides discussing the issue of how a process can be microscopically reversible and ...
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4answers
112 views

Definition of Entropy in thermodynamics

In most textbooks, the definition of entropy in reversible processes on a system $S$ is given simply as $$d S=\delta Q/T.$$ It seems to me this definition is insufficient since it does not specify ...
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110 views

“Violation” of the Second Law

I can't reconcile some facts about entropy and irreversibility. This depresses me, because I feel I can't quite grasp the importance of entropy. I will illustrate my problems with an example given by ...
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1answer
38 views

Can you choose the variables of a state function?

I'm confused. I was first introduced to entropy as a state function of internal energy and volume $$S(U,V) \Rightarrow dS = C_v\frac{\mathrm{d}T}{T} - p\frac{\mathrm{d}V}{T} $$ wich is the ...
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H-theorem and Boltzmann equation applied to Boltzmann distribution

Using the Boltzmann equation: $$ \frac{dH}{dt} = \int_0^{\infty} dr \int_0^{\infty} ds W(r,s)[p_r - p_s][\ln{p_r} - \ln{p_s}],$$ and assuming $p_r = e^{-\beta r}$, the equation looks like $$ ...
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1answer
67 views

Helmholtz free energy from a relation for entropy

The Legendre transformation defines the helmholtz free energy (at least according to my lectures) as: $F(T,V,N)=E-TS$ It also says to start with $E(S,V,N)$ and $T=\frac{\partial{E}}{\partial{S}}$ ...
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2answers
40 views

Entropy change at varying temperatures?

Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a specific temperature. Reversivility means that the temperature of the system must remain constant ...
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4answers
276 views

Difference between heat capacity and entropy?

Heat capacity $C$ of an object is the proportionality constant between the heat $Q$ that the object absorbs or loses & the resulting temperature change $\delta T$ of the object. Entropy change is ...
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1answer
71 views

Definition of entropy in nonequilibrium states

Thermodynamical definition of entropy $$S(p)=-\int p\ln p~dx$$ is defined only on equilibrium system. But why can't we use it for non-equilibrium system? Is there a well-accepted definition for it?
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1answer
47 views

Regarding the 'Arrow of Time'

I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their ...
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2answers
69 views

Why the amount of entropy increase to a system is less when heat is added to a higher temperature system than to a lower one?

As I understand it, statistically this means that a fall from a high temperature (say $300\text{ K}$) to a middle temperature ($200\text{ K}$), and an increase from say ($100\text{ K}$) to ($200\text{ ...
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Thermodynamics of scattering theory

I have a couple of conceptual questions regarding the thermodynamics of scattering. Any partial answer or argument will be appreciated. For the sake of discussion, consider the scattering of ...
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3answers
84 views

Is there a minimum energy content of information, other than 0 Joules?

Lets say I want to send the bit string 010110 to someone. Is there a theoretical lower bound on the energy needed to do this?
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2answers
154 views

Is the second law of Thermodynamics an immense tautology?

Let's imagine for a second a system that is changing constantly from one microstate to another one. It could be a given volume of a gas with its atoms moving and bouncing around, or a deck of cards ...
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1answer
52 views

Does the entropy of a system vary in the equilibrium?

I am not physicist and this question may seem trivial. But I understand that in the equilibrium the magnitudes such as temperature or volumen do not vary. Is the same for entropy? My logical says that ...
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297 views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
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41 views

Entropy of an oscillator in Einstein's solid

This is a homework problem and I need help with it. A solid's (Einstein's model) oscillators are in the first excited state on average. How much entropy does one oscillator have? What I've tried so ...
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1answer
121 views

Gravity and the Second Law of Thermodynamics [duplicate]

I was wondering about the hypothetical - and apparently improbable - heat death of the Universe when I stumbled upon this seeming contradiction. A certain volume of space with a uniform distribution ...
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2answers
130 views

Who invented the perfume bottle thought experiment?

A common thought experiment used to explain the second law of thermodynamics, the "arrow of time", etc. is perfume escaping from an opened perfume bottle; the perfume is likely to diffuse into the ...
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1answer
140 views

Thermodynamics for Dummies: Entropy and temperature

I do not study physics and I have never had a course in thermodynamics. I have no idea what it is about, but I am currently taking a course where we had something about entropy. Would be great if ...
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3answers
108 views

Is Fourier's law of conduction a consequence of the second principle?

In classical thermodynamics courses, entropy is often motivated by the need to justify that heat flows from high temperatures zones to lower temperatures zones: this is seen as a consequence of ...
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2answers
68 views

Dimensionless entropy interpretation

Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious ...
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5answers
231 views
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How does dark matter collapse?: Entropy considerations

Inspired by this question. I believe that the usual explanation that preserves the second law of thermodynamics as an astrophysical gas cloud collapses under gravity is that the gas must heat and ...
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3answers
144 views

Are galaxies, stars, planets, and ultimately life in violation of the second law of thermodynamics? [duplicate]

How can we think about entropy in these situations? To my knowledge all of these structures are born out of gravitational interaction. However, it would seem that the formation of these more organized ...
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9answers
2k views

What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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2answers
69 views

What is entropy of the universe? [duplicate]

What is entropy of the universe? What is the change in entropy of our universe? Is this change increases or decreases? If the entropy of universe keeps on increasing then what are the consequences? Is ...
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BTZ Black Hole Central Charge and Conformal Weight

I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
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3answers
99 views

Potential energy & entropy of three particles

Let me first say that I am not a physicist, but I am trying to make a simulation on my computer and I have the following question. Let's consider that we have three free charges that somehow can ...
2
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2answers
103 views

How can heat turn into light

I am confused about how hot surfaces can radiate light to their surroundings. When I shine a light on a surface the light turns to heat spontaneously, and when I leave that hot surface it radiates ...