Entropy Definition and 999 Threads

Summary:: An elementary example calculation involving entropy in a textbook seems wrong I was reading an elementary introduction to entropy and the second law of thermodynamics. The book gave the example of a gas in a chamber suddenly allowed to expand into an additional portion of the...

Per the Heisenberg uncertainty principle, a particle does not have a precisely defined location. Does such uncertainty contribute to the transfer of thermal energy (i.e. entropy)? Is uncertainty the primary means for the transfer of thermal energy at the quantum level?

Homework Statement:: Why is the entropy of a closed system constant in a reversible process, and not related by ##\Delta S = \int_{i}^{f}\frac{dQ}{T}## (See below for the question in more details) Relevant Equations:: ##\Delta S = \int_{i}^{f}\frac{dQ}{T}## I am reading chapter 24 of Physics...

Wasn’t sure whether I should post this here since it’s a more qualitative question, or under the Thermodynamics thread because that’s a more specific topic. For all practical purposes, the laws of thermodynamics are inviolable, and statistical mechanics puts them on an even firmer theoretical...

Hi, starting for this thread Question about entropy change in a reservoir consider the spontaneous irreversible process of heat transfer from a source ##A## at temperature ##T_h## to another source ##B## at temperature ##T_c## (##T_h > T_c##). The thermodynamic 'system' is defined from sources...

I always got a bit confused when listening to podcasts about arrow of time and entropy in the universe. So I was reading more about information theory. I learned today that for physical systems entropy is not defined. All it means is how much uncertainty an observer has when making a prediction...

Through an intriguing fictitious dialog between Sadi Carnot and Robert Sterling, Prof. Israel Urieli of the Ohio University shows that it is not required to invoke entropy, the second law of thermodynamics, and the Carnot cycle with the [ideal] adiabatic processes in order to find out the...

In chemical reactions generally ΔG < 0 , but if we were to consider a reversible path between pure reactants and products at 1 bar pressure , shouldn't the ΔG = 0 for every reaction ? and if it is due to non-pv work , I don't see any non pv work being done in reactions happing in a closed...

I know the math behind these, and I'm happy to use more precise language if needed, I just wanted to get some input on this sweeping generalization that entropy is the conversion of potential to kinetic energy. A brief summary of two important branches of entropy: 1) thermodynamics - the total...

I have been reading about protein thermodynamics and found different types and models for entropy calculation before and after protein folding. I understand Vibrational, conformational, configurational entropy are some of the most studied "types" of protein folding entropy. My questions is...

Hello, I am a 15 year old who has done research around the topic of why the universe is expanding at an accelerating rate, and how it will come to an end. After years of thought (since I was 11) I have come up with my hypothesis that time itself is accelerating and slowing down, and has been...

So for a collection of particles each with mass m, the pressure beneath them, ##p(z)## should be higher than the pressure above them ##p(z + \Delta z)##. This is a change in force per unit area (force per unit volume I suppose) times a volume to equate with the gravitational force $$ \frac...

Can we make sense out of the formula of entropy like we do for density (like "quantity of mass per unit volume")? What's the sense of Q/T? Couldn't it be something else? Of course it probably is a 'me-problem', but I haven't studied Thermodynamics deeply yet and was wondering what Entropy...

Hello, everyone :). I try to resolve this common problem. But, when i got in the interpolation of state 2, the values not make the sense. I have 25 psia and 75 F, but, in the superheated water table, there are not values with 25 psia (only 20 psia and 40 psia). And, the temperature values...

So just by by using the definition of the partition function... $$ Z = \sum_i e^{ \frac {-E_i} {k_BT} } = e^{ \frac {-0} {k_BT} } + e^{ \frac {-\epsilon} {k_BT} } = 1 + e^{ \frac {-\epsilon} {k_BT} } $$ And then, a result we obtained in class by using the Boltzmann H factor to solve for ##S##...

I am trying to understand how visually salient features could be discovered by unsupervised learning. I do not want to assume that we already have edge detectors or convolutional neural networks, rather I am trying to imagine how these could be discovered by observing the world. Imagine that a...

Summary:: Proving that entropy change in mixing of gas is positive definite > >An ideal gas is separated by a piston in such a way that the entropy of one prat is## S_1## and that of the other part is ##S_2##. Given that ##S_1>S_2##, if the piston is removed then the total entropy of the...

a) ##T_A=\frac{p_AV_A}{nR}=300.7K, P_A V_A=kL^2=nRT_A##, ##P_B S=k\frac{L}{2}\Rightarrow P_B V_B=k(\frac{L}{2})^2 \Rightarrow P_B=\frac{kL^2}{2V_A}=\frac{P_AV_A}{2V_A}=\frac{P_A}{2}##, ##W_{spring\to gas}=\int_{L}^{L/2}kxdx=-\frac{3}{8}kL^2=-\frac{3}{8}nRT_A####\Rightarrow Q=L+\Delta...

a) ##P_f=\frac{nRT_f}{V_f}=\frac{nR\frac{T_i}{2}}{2V_0}=\frac{1}{4}\frac{nRT_i}{V_0}=\frac{1}{4}P_i## b) ##Q=\Delta U=nC_V \Delta T=n\frac{5}{2}R(-\frac{T_i}{2})=-\frac{5}{4}nRT_i=-\frac{5}{4}P_i V_0## (##L=0## since the gas expands in a vacuum;Now, (a) and (b) are both correct but not (c), for...

By using the given relationship that S=a/T --(1) along with the equation ∫ (delta Q rev)/T=∫dS -- (2) I found out that my answer for the value of Q is mc*ln (T2/T1)*a upon equating (1) & (2). But the solution is instead given as Q=a*ln*(T1/T2). I would be grateful if someone would point out...

Which is a higher entropy state: solar system as it is today with planets going around the sun at fixed distances in an orderly fashion OR all the planets and sun bumping into one another and forming a single body? If the entropy of the combined single body is higher, why doesn't the solar...

Upon seeing the question in my assignment I knew in a isobaric process, work done by the gas is ##W=P\Delta V## so if volume is increased ##4## times the original considering the original volume as ##V## we can say after expansion the volume is ##4V##. Then ##W=P(4V-V)=3PV## and the ##Q## would...

I'm no expert but, as I understand it, in an open system, one that can take in energy and matter from outside of itself, the overall entropy level can be prevented from increasing (and can actually decrease) under the right conditions. I have three questions: 1. Can the kinds of quantum...

In many cases, the concentrations of defects or charges are quite big enough to use SA, due to a big number of Avogadro's number. The derivation for the well-known formula of a defect concentration is followed. If the n_v is expected to be lower than 1, then it would be impossible to use SA...

I wonder how physicists who support this theory explain the increase of entropy?

Hello, just wanted to ask regarding the otto cycle; if we were to find the entropy at the phase of isentropic compression and I was already able to derive the temperature 1 and 2 and the pressures at 1 and 2 and I also have the compression ratio of 10. How do I derive the entropy (s1 and s2)...

On page 50 of "From eternity to here", Sean Carroll writes that the protostellar cloud had a lower entropy than the solar system it produced. That strikes me as odd. A solar system looks more arranged than a dust cloud. When talking about entropy, someone always mentions the milk in the coffee...

I have heard from a knowledgeable physics proffessor, time exists independently and it is not a consequence of arrow of time. Could some body explain this?

Hi everyone, I have a fundamental question to the first part of Swendsen's Intro to StatMech and Thermodynamics (book). Suppose we have two isolated systems of volumes ##V_1## and ##V_2##. We distribute ##N## ideal gas particles across the two systems with total energy ##E##. Suppose we bring...

I have a simple question sort of about exact differentials and deciding which variables matter and when. I know we can write entropy ##S## as ##S(P,T)## and ##S(V,T)## to derive different relations between heat capacities ##C_V## and ##C_P##. I was wondering if it is technically correct to...

Hello! Could you please recommend me some good books about entropy for physics enthusiasts (someone who doesn't know physics but wants to learn about this)? Thank you!

Hi All, I would like to know how can one connect the two definitions of entropy ##\Delta S = \int_{T_i}^{T_f} \frac{dQ}{T} ## and ##\Delta S = k_B \ln (\frac{W_f}{W_i})##, particularly I am interested in how the logarithm emerges. Does it have to do with some linear dependence of the heat with...

Hey guys! This is problem from Callens Thermodynamics textbook and I'm stuck with it. My goal was to get a expression for the entropy ##S## which is dependent on ##T## so I can move into the ##T-S##-plane to do my calculations: I startet by expressing the fundamental equation as a function of...

In classical statistics, we derived the partition function of an ideal gas. Then using the MB statistics and the definition of the partition function, we wrote: $$S = k_BlnZ_N + \beta k_B E$$, where ##Z_N## is the N-particle partition function. Here ##Z_N=Z^N## This led to the Gibb's paradox...

One of the most fundamental equations in chemical thermodynamics states: $$ \Delta_rH_m^⦵ = \Delta_rG_m^⦵ + T \Delta_rS_m^⦵ $$ If we look at this equation in context of net chemical reaction in electrolytic or galvanic cell, it is usually interpreted as follows: Enthalpy of reaction denotes...

Hey guys! I'm currently struggling with a specific thermodynamics problem. I'm given the entropy of a system (where ##A## is a constant with fitting physical units): $$S(U,V,N)=A(UVN)^{1/3}$$I'm asked to calculate the specific heat capacity at constant pressure ##C_p## and at constant volume...

So what I did was find the change in Q per min. Mass melted per min * latent heat capacity = Q per min = 11.5 kg /min * 3.4*10^5 J/kg = 3910000 J/min Now the equilibrium temperature is 100 degrees Celsius or 373.15 degrees kelvin. If I do 3910000 J/min / 373.15 K I get 10478 J/(K*min). This...

In the industry, coal and other fuels are typically represented by - their C, H, O, N, S elemental composition for the combustible part - the composition of the ashes (SiO2, Al2O3, Fe2O3, ...) - the Low Heat Value (LHV) which is the heat that can be extracted from combustion product With...

Context Boltzmann first defined his entropy as S = k log(W). This seems to be pretty consistently taught. However, the exact definitions of S & W seem to vary slightly. Some say S is the entropy of a macrostate, while others describe it as the entropy for the system. Where the definition of...

It looks very easy at first glance. However, the variable S is a variable in the given expression. I have no clue to relate the partial derivatives to entropy and the number of particles.

Is the purpose of the 0th, 1st & 2nd Laws of Thermodynamics simply to legitimate the thermodynamic properties of Temperature, Internal Energy & Entropy, respectively? It seems that all these laws really do is establish that these properties are valid thermodynamic state properties and the...

In the book for our thermodynamics, it states that a process that is internally reversible and adiabatic, has to be isentropic, but an isentropic process doesn't have to be reversible and adiabatic. I don't really understand this. I always thought isentropic and reversible mean the same thing...

I've calculated the change in the entropy of material after it comes in contact with the reservoir: $$\Delta S_1 = C \int_{T_i+t\Delta T}^{T_i+(t+1)\Delta T} \frac{dT}{T} = C \ln{\frac{T_i+(t+1)\Delta T}{T_i+t\Delta T}}$$ Now I would like to calculate the change in the entropy of the...

We know that $$dU=\delta Q + \delta W$$ $$dU = TdS - pdV$$ So from this: $$dS = \frac{1}{T}dU + \frac{1}{T}pdV \ (*)$$ For an ideal gas: $$dU = \frac{3}{2}nkdT$$ Plugging that into (*) and also from ##p=\frac{nRT}{V}## we get: $$S = \frac{3}{2}nk \int^{T_2}_{T_1} \frac{1}{T}dT +...

I have been able to get everything except entropy. I know it's not zero. I know I have to find a reversible path to calculate it, but keep coming up with strange values so I don't think I'm doing it correctly. can I do CpdT/T + CvdT/T = ds? I am having trouble calculating my P2 (I know my final...

I have used the Lagrange multiplier way of answering. So I have set up the equation with the constraint that ## \sum_{x}^{} p(x) = 1## So I have: ##L(x,\lambda) = - \sum_{x}^{} p(x)log_{2}p(x) - \lambda(\sum_{x}^{} p(x) - 1) = 0## I am now supposed to take the partial derivatives with respect...

Does anyone have any thoughts on this book? https://www.amazon.com/dp/9813234121/?tag=pfamazon01-20

I understand entropy as a movement from order to less order and that the universe's entropy is increasing. So I was wondering, life takes molecules and organizes them into organisms, so isn't life a reversal of entropy?

When trying to describe why the entropy goes up for a irreversible process, such as gas expanding into a vacuum, it seems fairly easy at a high level. the valve between the two chambers opens, the free expansion occurs, the pressure drops proportional to the volume change and the temp remains...

I'm reading Brian Greene's latest book 'Until the End of Time' (I'll pause here while you finish groaning at yet another layperson reading popularist physics books.) In it, he's describing entropy in a way I've never heard before and it clarifies something that's always stuck on my craw about...