Entropy Definition and 999 Threads

Homework Statement Are the Gibbs and Boltzmann entropies always equivalent? Homework Equations $$ S=k_{B}ln\Omega $$ [Boltzmann entropy, where ##\Omega## is the number of available microstates $$ S=-k_{B}\sum_{i}p_{i} ln(p_{i}) $$ [Gibbs entropy, where ##p_{i}## is the probability of a...

Hi all, 1. Homework Statement A system of non-degenerate multi-level atoms are all in their lowest energy state. Calculate the entropy of the system. Homework Equations S = kbTln(Ω) S = Q / T dU = TdS - pdV The Attempt at a Solution I'm not sure how to proceed. I know that Ω is the...

All of my information comes from my current chemistry class, I just want to know where I either may have misread, misinterpreted, or was mistold information. With the 2nd Law of Thermodynamics we can say $$[1]\space\space \Delta{S}_{universe} = \Delta{S}_{surroundings} + \Delta{S}_{system} >...

Homework Statement (a)How much heat must be added to a block of 0.120kg of frozen ammonia initially at 100oC to convert it to a gas at 80oC given the following information? (b) assuming this could be done using a reversible process what would be the total entropy change associated with this...

I am looking to walk trough hawking and beckenstien's arguments for the proportionality of bh entropy to surface area to better understand black hole entropy. Does anybody know where I can find this calculation? I have taken relativity and qft so I am comfortable with this level of difficulty.

It seems to me that Gibbs' Paradox (that the entropy of a classical ideal gas, calculated by phase-space volume, is not extensive) can be resolved without assuming that particles are indistinguishable. Suppose instead the opposite: that particles are distinguishable, meaning that each one can...

This may be a matter of me being confused by the definition of heat. However, I view heat as the energy passed between systems of different temperatures. My problem is the following: By the principle of minimum energy/max entropy, in an isolated system (and therefore fixed internal energy)...

This may not make sense but I'm going to throw it out there in hope of some suggestions. If I have a system, for simplicity say particles in water and they are subject to a flow of some kind, as the flow is increased it becomes more turbulent and the particles are flying around all over the...

Homework Statement In an adiabatic container are placed , in rapid succession , a mass of ice , ##m_I= 2 kg## , at temperature ##T_I = -10 ◦C## and a mass of water , ##m_W = 1 kg## , at the temperature ##T_W = + 20 ◦C## . Determine : a) the total mass of water present in the container at...

What is the change in entropy of thermodynamic environment if it changes its temperature during the process and the process is not reversible? I'm slightly confused because, on the one side, in that case ##\Delta S_{gas} \neq -\Delta S_{surroundings}##, since ##\Delta S_{universe} >0## but on...

I have a question regarding the two seemingly different phenomenon of gravity and entropy.I want to ask that exactly how the gravity and over-all entropy of the universe are related?The thing that came to my mind is that could gravity be not a fundamental force of nature at all? Could it be a...

Homework Statement The following data refer to an electrically operated refrigerator: - Efficiency : ## \xi = 2.4## - Temperature inside: ##T_i = -9 ° C ## - Temperature of the radiator ## T_r = 40 °C ## - Room temperature: ## T_s = 35 °C## - Total surface of walls: ## A = 3.2 m ^ 2 ## -...

I don't get this concept at all. I am also confused on what entropy is at all. I have always thought of it as the measure of disorder but this seems to be only one of the definitions. Maybe it's because I'm not sure what entropy is that I am having a problem with understanding reversibility...

Dear all, I'm trying to think about applying the second law of thermodynamics to a system which is not isolated, but has an energy flowing inwards and an equal (!) energy flowing outwards, such that the total energy does not change (total energy flux is zero). Can we still apply the second law...

Given a sample of nitrogen gas (assume ideal gas conditions), the following conditions were observed inside the container. n = 0.75 moles at 253 K, and pressure = 0.5 atm. Then, an ISOTHERMAL IRREVERSIBLE COMPRESSION on the system forced by a constant Pexternal = 10 atm reduced the initial...

I was reading about entropy, Poincare recurrence theorem and the arrow of time yesterday and I got some ideas/questions I'd like to share here... Let's think a about a system that is a classical ideal gas made of point particles, confined in a cubic box. Suppose that at time ##t=0## all the...

If there is enough gravity and the universe starts to collapse in on itself, would life forms that live during this phase of the universe get younger as time passes and they would need to expend energy to stay old?

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?

Considering a closed system with an ideal gas(in a low entropy state) inside, then are following statements correct? The gas is in a certain state we can assign an entropy value to. Let X be the set of all states which are of a lower entropy value compared to the current state. Y the set of...

Layman question here. I have often read that the known laws of physics, QM and Relativity, do not make a difference between past and future, they are perfectly reversible in time. The only fact which gives time its preferred arrow is the 2nd Law, the increase of entropy, which manifests in the...

I have some doubts on entropy change of certain simple process. Can you check if these statements are correct? This is what I know: For a reversible adiabatic process, $$\Delta Q=0$$. $$\Delta S_{system}=\frac{\Delta Q}{T}=0$$. Since the system does not alter the surroundings, ##\Delta...

Homework Statement Calculate the entropy changes of the system and the surroundings if the initial and final states are the same as in part a ( part a= 2.000 mol of neon (assume ideal with CV,m _ 3R/2) is expanded isothermally at 298.15K from 2.000 atm pressure to 1.000 atm pressure and is...

If we consider a system to undergo an irreversible process from state 1 to state 2 and a reversible process from state 2 to state 2, then through Clausius inequality (1to2∫dQirrev/T) + (2to1∫dQrev/T) ≤ 0 (1to2∫dQirrev/T) + s1 - s2 ≤ 0 s2-s1 ≥ (1to2∫dQirrev/T) Δs ≥ (1to2∫dQirrev/T) Does this...

Homework Statement Two isolated containers, of volumes V1 and V2, enclose ideal single atom gas at the same pressure p. The number of particles in each container is equal, the temperature of gas in container one is T1=293K and the temperature of gas in container two is T2=308K. An equilibrium...

Homework Statement A bottle with volume v containing 1 mole of argon is next to a bottle of volume v with 1 mole of xenon. both are connected with a pipe and tap and are same temp and pressure. the tap is opened and they are allowed to mix. What is the total entropy change of the system? Once...

qrev/T = ΔS here what does ΔS signify?does it mean change in entropy of system or surroundings? how is entropy of system,surrounding and universe related to each other and which entropy is used in gibbs free energy equation?

What is the difference between Q=m(u2-u1) + W & Q=m(h2-h1)? Basically I am trying to figure out 2 different sets of questions and apparently using these separate equations yield different answers, and I don't know which equation to use. From my understanding, both of them are used in...

I have attached two images from my textbook one of which is a diagram and the other a paragraph with which I am having problems. The last sentence mentions that due to violation of 2nd law we cannot convert all the heat to work in this thermodynamic cycle. However what is preventing the carnot...

For all adiabatic processes the entropy of the system does not change (speaking in general) Is this statement correct?

Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...

My lecturer claimed that "reverse entropy stars" could exist in our universe. One of the examples he gave was that if you exposed some sort of detector in the direction of a hypothesized reverse entropy star, you could determine if it existed by whether it "sucked" photons out of the detector...

Dear PF Forum, I'm trying to make sense about Hawking radiation in Black Hole. And that leads me into entropy. I read this equation in https://en.wikipedia.org/wiki/Entropy What does that mean? S is the change of Entropy What does Qrev mean there? Is it in Calorie? then Joule? T, I think is in...

Homework Statement Consider a D dimensional Ising model with N sites, defined by the Hamiltonian $$\mathcal H = -J \sum_{\langle i j \rangle} \sigma_i \sigma_j - h \sum_i \sigma_i$$ where the sum extends over nearest neighbours and each spin variable ##\sigma_i = \pm 1##. For a given spin...

Homework Statement Consider a closed, adiabatic system consisting of a mixture of liquid and solid substance Z at equilibrium at its melting point. Z (solid) <---------> Z (liquid) Which of the following statements is true regarding the system? A) The entropy of the system is at a maximum...

1. I understand an expanding gas has increasing entropy and at a cosmic scale the universe is an expanding gas...sort of. 2. back before the universe was cool enough to form atoms it would seem to be very disordered, ie a high temperature universe of a plasma made of nuclei and elementary...

I have the following program that simulates a stochastic system of 400 particles. What I want to do now is separate the 200x200 grid into 2x2 smaller grids, out of which I will calculate each probability: P_i= \frac{\sum_{\text{atoms}}}{4} and from which in each step I'll be able to determine...

Homework Statement Hi ! I'm stuck with these two questions of my assignment of thermodynamics - Give two exemples of irreversible process (initial state, process, final state) - For each of them, explain why they are irreversible on the microscopic scale. Homework Equations We are not asked...

Homework Statement A turbine is receiving air from a combuster inside of an aircraft engine. At the inlet of the turbine I know that T1 = 1273 K and P1 = 549 KPa, and the velocity of the air is essentially 0. The turbine is assumed to be ideal, so its efficiency is exactly 1. Also: R = 287...

Entropy is basically a measure of the number of avaible microstates a system can have, given a certain energy of the system. It is a measure of the uncertainty of the exact state of the system. Now, suppose we have a box with a single particle inside and with the only internal energy being the...

Homework Statement A sample consisting of 1 mol of a diatomic perfect gas with Cv,m = 3/2 R is heated from 100 ºC to 300 ºC at constant pressure. Calculate ∆S for the system. Homework Equations Cv,m = 3/2 R The Attempt at a Solution Cpm=Cvm +r because we want cp right isobaric ∆S= Cp ln...

is entropy problem easiest than quantum mechanics problem which one is more complicated to understand and to solve ?

I have heard that identical distinguishable classical particles having different ''statistics''.It is the limit of quantum case.Then we mix many parts(cells) of identical gases, the total entropy increases.I can not derive this limit from quantum particles to classical particles(please help...

Hi I'm having some trouble understanding Shannon entropy and its relation to "computer" bits (zeros and ones). Shannon entropy of a random variable is (assume b=2 so that we work in bits) and everywhere I've read says it is "the number of bits on the average required to describe the random...

Homework Statement Two rigid, insulated tanks are connected with a pipe and valve. One tank has 0.5 kg air at 200 kPa, 300 K and the other has 0.75 kg air at 100 kPa, 400 K. The valve is opened, and the air comes to a single uniform state without any heat transfer. Find the final temperature...

Is there any theory that says anti-information exists? If there is anti-matter, would that matter carry information to annihilate the regular matter's information saying its a certain type of matter and turn it into energy? Could anti-matter just be regular matter with anti-information.

Hello all. I have a quick question about entropy... I've just been formally introduced to it. Consider the example of a metal block of mass m and heat capacity Cp at temperature T1 = 60C being dropped into a large lake of temperature T2 = 10C. $$\Delta S_{block} =...

Homework Statement The entropy change of surrounding is greater than that of the system in a/an (A) exothermic process (B) endothermic process (C) both (A) and (B) are correct (D) none of these are correct Homework EquationsThe Attempt at a Solution ΔStot = ΔSsys + ΔSsurr For a spontaneous...

Hi all, I'm having some trouble figuring out why entropy is used instead of enthalpy for an open system. From what I understand, an open system uses entropy to calculate internal energy. Since the control volume is constant (i.e. Δv = 0), wouldn't using : h = u + PΔv effectively be h = u? So...

Hello, I am learning about using Free energy change /delta G to determine if a chemical reaction will occur spontaneously. /delta G = /delta H + T*/delta S. Now, enthalpy change can drive a reaction which leads to a decrease in entropy (multiple reactants => single product). My Question...

Homework Statement A 1 liter container is filled with argon to pressure of 10^5Pa at 303K. Dropped into pool at temp 323K. How much heat is needed to heat the gas to 323K? what is the entropy change in the gas and the universe? ignore the entropy change in container. Homework Equations...