Entropy Definition and 999 Threads

Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - Tr[\rho ln \rho] = H[\lambda (\rho)] $$ where ##H[\lambda (\rho)]## is the Shannon entropy of the set of probabilities ##\lambda (\rho)## (which are eigenvalues of the density operator ##\rho##). Definition 2 If...

Well, maybe that's a simple question, but it has been pissing me off for some time ... Does entropy increase with improbability?

It is assumed that entropy increases in the universe. However, the fluid and acceleration equations are derived assuming that. TdS=dE+pdV where dQ = TdS. But dQ is usually set equal to zero to derive these equations. Hence since T is non zero, dS should be zero and so there would be no...

Every year since the 90's I come back to some of my pet topics in physics, like statistical physics. This time it was the reading of a Wikipedia article on entropy that surprised me. The derivation of the second law from the Gibbs entropy was unknown to me. I didn't know how heat, how change of...

Homework Statement A 2.45 kg aluminium pan at 155 C is plunged into 3.58 kg of water. If the entropy change of the system is 162 J/k, what is the initial temperature of the water? Homework Equations Q = mcΔT ΔS=mcln(T_2/T_1) Q_water + Q_Aluminium = 0 c water = 4184 J/kg*K c aluminium = 900...

Homework Statement Find the ∆S per mol between liquid water at -5 ºC and ice at -5ºC at 1020hPa Data: ∆CP,m fusion = 37,3 J K-1 mol-1 ∆fusH = 6,01 kJ mol-1 The answer is 21.3 J/K mol Homework Equations Usually I solve these problems by steps when they are at P=1 atm but since its at P=1020...

Hi, I am quite confused about followed question, I think scientist think the last scattering surface was dense plasma at the temperature of 3000K. If the today's universe much cooler and less dense then "the last scattering surface" how can anyone says entropy increased by time? Isn't universe...

Homework Statement Homework EquationsThe Attempt at a Solution ## dS = \frac { dQ_{rev} } { T } ## Assuming that isothermal process is a reversible processes, ## dU = dQ – pdV## For isothermal process, dU = 0. ## dQ = pdV ## ## pV = nRT##, where n is number of moles. For one mole, ##...

Homework Statement I am Pretty Lost with this problem...[/B] A 2.45-kg aluminum pan at 155∘C is plunged into 3.58 kg of water. If the entropy change of the system is 162 J/K, what was the initial temperature of the water? NOTE:We did not receive a Tf for the system. Homework Equations...

Thermodynamics is stated in different ways. E.g. In isolated systems entropy never decreases Heat never spontaneously pass from colder to warmer body Total energy quality decreases in all processes. Energy disperses But what is it exactly? What is the correct description of the 2nd law of...

Homework Statement A system having ##N## non-degenerate energy eigenstates populated by##N## identical spin-zero particles and ##2N## identical spin-half particles. There are no interaction between any of these particles. If ##N=1000## what is the entropy of the system? Homework Equations...

Homework Statement I came across this equation ##L / T = \Delta S## and am not too sure about its derivation. From what I know, ##L = Q/m## and ##Q = TdS ##. Substitution gives me ##\Delta S = mL / T## which isn't correct. Could someone assist me in understanding the derivation? Thanks...

I read this discussion but I am interested in how the entropy is obtained as a function of pressure. Namely, how can you determine a following integral for an ideal gas: $$S(p) = -\int_{0}^{p} \frac{nR}{p}dp $$ when you need to start from 0 pressure?

As I understand it, horizons, such as black hole or cosmological event horizons is a place where time seems to stop. So if nothing changes at the horizon, then can there be entropy there? Does entropy require things to change with time? If not energy dissipates because nothing moves, then what...

Homework Statement A container of 1.5 Kg of gas is at a temperature and pressure of 293 K and 1 bar respectively. The gas is adiabatically compressed until its temperature and pressure are 450 K, 4.49 bars. Adiabatic processes are processes with no heat transfer. The properties of this...

Homework Statement Calculate q, w, ∆E, and ∆H for the process in which 93.0 g of nitrous oxide gas (N2O) is cooled from 179°C to 55°C at a constant pressure of 4.00 atm. Cp(N2O) = 38.70 J K-1 mol-1 Homework Equations q= mCΔT ΔH=n(Cp)=n(qv)ΔT ΔE=q+w w= -pΔV *Probably something else too but I'm...

I have a question regarding the process of getting towards equilibrium in our universe. If we imagine a causal patch with our planet at the centre, every planet will redshift away from us an after a while the planet itself will disintegrate, let's call this process the decay of Earth. Eventually...

Homework Statement [/B] Phospine exist in three forms. known as the \alpha, \beta and \gamma forms. The \alpha and \beta forms are in equilibrium with each other at 49.43 \, K, and the \alpha and \gamma forms are in equilibrium at 30.29 \, K. Obtain the molar heat of transformation for the...

Homework Statement Two vessels A and B each contain N molecules of the same perfect monatomic gas. Initially, the two vessels are thermally isolated from each other, with the two gases at the same pressure P and at temperatures T_A and T_B. The two vessels are now brought into thermal contact...

Homework Statement Two systems that have the same heat capacity Cv but different initial temperatures T1 and T2 (with T2 > T1) are placed in thermal contact with each other for a brief time, so that some heat flows but the temperature of neither system changes appreciably. Show that there is a...

Homework Statement Show that \Gamma_T is maximum at E_a = \frac{N_aE}{N_a+N_b} Homework Equations The expression for \Gamma(E) when N\gg 1 \Gamma_T = C_aC_b exp \left( -\frac{E_a^2}{2N_a\mu_B^2h^2} \right) exp \left[ - \frac{(E-E_a)^2}{2N_b\mu_B^2H^2} \right] where C_a and C_b are...

Homework Statement Homework EquationsThe Attempt at a Solution I didn't understand the last part. At eqbm. ##\Delta S = 0##. This means that the RHS of the eqnn. 14.25 is 0. This doesn't mean that the following eqns. must hold true. ##(\frac 1 T_1 - \frac 1 T_2) =0,.............(1) \\...

I'm interested in classical and quantum entropy. Is there a section on PF devoted exclusively to this topic? I searched a few forum discussions but couldn't find anything. I'm new here. Thank you.

Homework Statement The question is: What happened with the entropy in a free expansion? The system is isolated and the state equation is: $$p=AT/V+B/V^2$$ Homework Equations $$dU=TdS-pdV$$ The Attempt at a Solution My attempt is: Because the system is isolated and corresponding to an free...

1. Robert Dehoff 4.12 A system is designed that permits continuous programmed control of the pressure and volume of the gas that it contains. The system is filled with 1 g atom of helium and brought to an initial condition of one atmosphere and 18 liters. It is then reversibly compressed to 12...

Is it ok to assume that the entropy ##S## of an arbritary system can be written as a power series as a function of the system's internal energy ##U##? Like $$S(U) = \sum_{i=1}^{\infty}a_iU^i = a_1 U + a_2 U^2 + \ ...$$ with ##a_i \in \mathbb{R}##. What results could be obtained from such...

Homework Statement Homework Equations $$\frac{\partial S}{\partial u}\Bigr|_{v} = \frac{1}{T}$$ $$\frac{\partial S}{\partial v}\Bigr|_{u} = \frac{-P}{T}$$[/B] The Attempt at a Solution a.) $$\frac{S}{R} = \frac{UV}{N} - \frac{N^3}{UV}$$ $$\frac{S}{R} = \frac{UV}{N} - \frac{N}{uv}$$ $$...

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?

How much correct to say entropy is always measure of disorder Is disorder always related to entropy

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?

I'm wondering about the exact usage of the term entropy in programming vs. entropy in science.

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...

ShayanJ submitted a new PF Insights post Entanglement Entropy – Part 2: Quantum Field Theory Continue reading the Original PF Insights Post.

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...