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Questions tagged [entropy]

An 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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$\dot{W}_{lost}$ due to irreversible processes in a refrigeration unit

The condenser of a refrigeration system steadily admits $\dot{m} = 50 g/s$ of saturated R134a with a pressure $P_1 = 650kPa$ and a quality $x_1 = 0.9$. The condenser rejects $\dot{Q} = 7kW$ of heat to ...
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Confusion with entropy change associated with thermal reservoirs in an isobaric process

On chapter 8, Entropy, Zemansky and Dittman's book Heat and Thermodynamics has a problem with following details: A body of constant heat capacity $C_p$ and at a temperature $T_i$ is put in contact ...
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Entropy and equilibrium concepts at astronomic scales

I am always puzzled to read here and there discussions dealing with thermodynamic concepts applied to astronomic scales where gravity matters. To my opinion, there is a certain carelessness to go into ...
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Can anyone explain equivalence of statistical entropy and thermodynamic entropy?

I read on wikipedia how Clausius came to define entropy after studying the Carnot cycle (He found a relation between heat transfer and temperature which was a state function,and named it entropy) but ...
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Can indistinguishable microstates evolve into different macroscopic states?

I guess this question is more about definition than about any physical principle. Can a given physical system (or can there be a physical system) admit microstates that have identical macroscopic ...
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How to quantify the mixing of two hard-spheres gases?

Suppose that there are two types of hard-spheres gases ($a$ and $b$) in a box. Suppose that their radius is much smaller than the box's characteristic size. These two gases tend to repel each other. ...
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Why do we have to dump the extra entropy created in a heat engine?

In his introduction to thermophysics, Daniel Schroeder writes the following about the process in a heat engine: Only part of the energy absorbed as heat can be converted to work. The reason is, ...
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I reasoned that if $T_2 > T_1$ then $E_1>E_2$. Obviously this can't be right, what is the flaw in my logic?

We have an entropy function and I've shown that for this function $T_1(E_1)=T_2(E_2)$. Further, the fact that the entropy function is concave is stated. There are two systems in contact and only ...
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Is uncertainty and correlations actualy the same thing?

In this paper on page 2 it is said that The entropy $S(\rho_A)$ measures the amount of correlation (classical and/or quantum) between $A$ with the external world. Now this is confusing me a little ...
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On isentropic compression of ideal gases, work and internal energy

I'm trying to understand something about isentropic compression of Hydrogen. If you are assuming constant specific heats, the work done during an isentropic compression is $$W = \frac{k}{k-1}\cdot ...
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Derivation of Proportionality of Phase Space Volume log(Γ)∝N

In the derivation of extensivity of entropy for the micro-canonical ensemble, we assume an ensemble of two systems with the energies $E_1$ and $E_2$. The total energy is given as $E<E_1+E_2<E+\...
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What was the informational content of the universe at the Planck time?

If the energy of $1 \, \mathrm{bit}$ of information is $k_{\small{\text{B}}}T \ln{2}$, then the energy of that bit increases with the temperature of the system. When I try to calculate how much energy ...
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How do we quantify this kind of information in Quantum Mechanics?

Let a quantum system be given with Hilbert space $\mathscr{H}$. Suppose it is described by the quantum state $\rho$, i.e., a density matrix. We can define the Von-Neumman entropy as $$S(\rho)=-\...
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Prove Von Neumann entropy is invariant under coordinate transformation

https://en.wikipedia.org/wiki/Von_Neumann_entropy#Properties How to show that von Neumann entropy for $p_k$ with basis $|\psi_i\rangle$ is the same for $p_n$ with basis $|\phi_i\rangle$? That is, to ...
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Shock attenuation using Riemann invariants (shock rarefaction interaction)

I have been trying to use Riemann invariants to solve a rarefaction wave overtaking a shock wave. Has anyone had any luck with using Section 83 in Supersonic flow and Shock waves by Courant and ...
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Phase transitions and Helmholtz vs Gibbs Free Energy

Gibbs phase rule for Gibbs free energy says that phases during a phase transition must be in mechanical, chemical, and thermal equilibrium, e.g. $T_1=T_2$,$G_1=G_2$, and $P_1=P_2$, where the ...
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What additional percentage of the suns energy is being trapped via green house gases?

Every year we release more greenhouse gases which causes the atmosphere to trap more energy and thus warm the planet. What additional percentages of energy are we talking about here? I would assume ...
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Replacing Qh with Ql in Etropy equation in Heat Pump

In the heat pump below, the $T_H$ is not constant. It is assumes that the process is steady and reversible. So when constructing an entropy equation over the CV (the purple-colored area): $$\dot ms_1+\...
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Does Von Neumann entropy fail to account for projective quantum measurements?

I'm trying to understand if this line of reasoning is correct: For a two-state pure quantum system $\left|\psi \right\rangle=\frac{1}{\sqrt{2}} (\left|0 \right\rangle+\left|1 \right\rangle)$, The ...
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Would it be appropriate to say that in presence of Non-Conservative Forces, the Entropy of System Always Increases?

Would it be appropriate to say that in Presence of Non Conservative Forces the Entropy of a system would always increase? Can we relate Non-Conservative Forces and Entropy in some way? I intuitively ...
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Derivation of Helmholtz free energy and associated relation

I am quite new in thermodynamics and I have never touched it so far. But now I have some basic questions that I hope someone can kindly explain them to me. I know the Helmholtz free energy is ...
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Universal Entropy [duplicate]

I’m a first-time poster... Could entropy possibly be the reason the universe is expanding and even why its expansion is accelerating? If space is not surrounded by anything at all, it would seem to ...
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Does the uniqueness of Big Bang violate space-time homogeneity?

One possible way to explain the arrow of time is to say that the entropy is increasing simply because the entropy in the beginning was at unsustainably low levels and is therefore bound to increase. ...
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Breaking Stuff and Putting it Back Together

I was wondering if you could put something back together exactly the way it was before. It takes a certain amount of energy to break something, so theoretically could you put it back together exactly ...
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What is the relation between enthalpic and entropic forces?

I think of entropic force to be an entropy minimizing mechanism and the enthalpic force to be an energy minimizing mechanism (which is basically an entropy maximization mechanism). What's the ...
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Von Neumann entropy of a quantum state vs Von Neumann entropy of a system

Using the Chuang and Nielsen Quantum Computation and Quantum Information book, for an introductory course in Quantum Information, I stumbled on an ambiguous (at least for me) use of the Von Neumann ...
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$dQ=Tds$ and quasistatic process

See Ján Lalinský's commment on Entropy $dQ=TdS$ and Work $dW = -pdV$ conditions? My question are: Is there a way to prove that $dQ=Tds$ is a quasistatic process? What's the funcitonal description ...
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Computing entropy for two ideal gas systems

I'm trying to show the processes in the following rows are different. So on the left there are $12$ particles in each box with volume $V=V_1$. Both are divided in three imaginary and equal parts with ...
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Hydrodynamics, isocurvature and entropy

I am trying to figure out what happens in the following situation: You have a fluid that consists of many types of particles that can turn into each other via chemical or nuclear reactions such that ...
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Isentropic expansion and heat capacity [closed]

I am currently trying to learn some basics of thermodynamics. I encountered the following equation $$ \frac{p_2}{p_1}=\left(\frac{V_1}{V_2}\right)^\gamma $$ that allows computing the effect of an ...
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What causes a black hole to be hot?

From my limited understanding of physics, it seems that the heat of a black hole is caused by vibrations in quanta of space, where quanta of space can be viewed as the elementary building blocks of a ...
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Information to Energy equations?

Are there are any known formulas or equations that can calculate information from energy or energy from information? One of them, I believe, is the Bekenstein bound which is the maximum information ...
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How could the early Universe have low entropy when it was so compact? [duplicate]

Entropy of a system can be understood as "the number of states that are macroscopically indistinguishable from the state its currently in". (Sean Carroll, "The Big Picture") Given that the early ...
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Entropy vs Temperature Dependent Intermolecular Force

It makes obvious physical sense that whenever there is heat transfer amongst ideal gases, there is entropy generation. When the molecules are attracted to each other as is the case of real fluids (...
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How is a superconductor maintaining a persistent current a reversible process?

Once an electric current is established, and then the external electric field/voltage is withdrawn, a superconductor maintains the current forever. Such a process neither violates the first law nor ...
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Earth-like Atmosphere Breaks Second Law of Thermodynamics due to Conduction?

Consider a neutral gas around an Earth-like atmosphere with density, pressure and temperature given by $\rho,\ p$ and $T$ respectively. To keep the system a closed system assume that the atmosphere is ...
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Entropy calculation

A piston-cylinder device contains 1.2 kg of nitrogen gas at a 120 KPa and 27 degrees Celsius. The gas is now slowly compressed in a polytropic process during which pV^1.3= constant. The process ends ...
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How do you calculate the change in entropy for a non quasistatic process

I understand that Entropy is a state function, but the change in entropy does in fact depend on the process from a-->b. I understand the derivation for entropy where $$S_2-S_1=Ncv\ln\frac{T_2}{T_1}+...
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Ideal Work in adiabatic steady state flow processeses

For calculating ideal work: By applying entropy balance on a steady state flow process we get:- delta(S*mass flow rate) - (rate of heat transfer from system)/Tsurr = 0. Thus according to this ...
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How does the Second Law of Thermodynamics place limits on allowable heat transfers?

I'm confused by the following excerpt from my thermo book, which is referring to a heat engine in contact with two reservoirs: According to the first law of thermodynamics, the net work transfer is ...
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Entropy transfer between finite heat capacity systems

Consider two systems $A$ and $B$ in an insulated vessel with constant finite heat capacities $C_A$ and $C_B$, which are initially at different temperatures $T_{A1} \neq T_{B1}$ for the initial state $...
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Entropy generated for a warm bath heating a cold rock

Put a cold rock of heat capacity $C_r$ and temperature $T_{r1}$ into an insulated fluid bath of finite heat capacity $C_b$ (the bath is not a reservoir) and temperature $T_{b1}$. Now let the entire ...
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Reversible compression of a gas - faulty reasoning?

I am trying to figure out where my reasoning falls apart in this thought experiment: To determine if a process "A" is reversible (or at the very least internally reversible), I try to picture a ...
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Why is the formula for blackhole entropy different that the formula for entropy given by Boltzmann?

why are there different formulas for entropy? (the Boltzmann one and the black hole one given by hawking). entropy by Boltzmann is $S= k \log W$ entropy for a black hole is $S=zA$ where $A$ is the ...
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If information is conserved, why did the early universe had lower entropy than now? [duplicate]

If information and entropy are equivalent, and information is a conserved quantity because of unitarity, what does it mean to say that entropy is growing since the big bang (I know why it grows, I'm ...
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Finding an expression for isothermal compressibility from entropy $S(E,N,V)$

I am trying to find a way to find an expression got the isothermal compressibility ($\kappa_t$) and for the thermal expansion ($\alpha$) of a cristal that has an entropy function S(E,N,V). The entropy ...
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Where is the error in this change of entropy derivation?

The thermodynamic definition of entropy is $\mathrm{d}S \equiv \frac{\delta Q_{\mathrm{rev}}}{T}$ where $\delta Q_{\mathrm{rev}}$ is a strictly reversible "change" in heat. The second law of ...
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What is state variable and full differential? e.g. in entropy?

I am studying basic concepts of entropy and statistical physics. And red a lot what is entropy, and that it is integrative factor of heat; and getting it with the full differential._ Anyway, what I ...
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Exergy, entropy and energy quality

I'm teaching a class on the subject of "energy quality". I'm supposed to tell them that energy quality is a measure of how easily (effective I guess) the type of energy can be converted to different ...
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Why can't we plot irreversible processes on a $T$-$S$ diagram?

In the book "Heat and Thermodynamics" by Zemanky, It is stated that "only reversible processes can be plotted on a $T$-$S$ diagram. Since the definition of entropy involves a reversible change in ...