Thermodynamic Definition and 459 Threads

My professor said that F is not additive, meaning F ≠ F1 + F2, where F1 is the helmholtz energy of system 1 and F2 is the helmholtz energy of system 2. So my question is, how can I decide wether a thermodynamic potential (F, H, G) is additive or not?

I have a rather basic question regarding the chemical potential (##\mu##) in thermodynamics and its relation to the Gibbs free energy (##G##). All thermodynamics textbooks I've looked at (Landau & Lifshitz, Kittel...) derive the fact that, at constant temperature ##T## and pressure ##p##, the...

At first I thought these values should be equal because I thought thermodynamic work is simply the work done as the gas compresses or expands. That is, the work done as the gas expands ( and the mass gets lifted up) should be equal to the work done against gravity as the mass goes up, and the...

I am only interested in the initial equilibrium conditions, and I am struggling to convince myself whether that should correspond to the equality of chemical potentials for H2 or an equality of temperatures as well. My work is as below: We take both gases as simple ideal (this is only relevant...

First off don't quit reading if you understand basic Bernoulli effect. I am nowhere close to the caliber of minds on this forum but I have a problem and lack understanding that science may help answer. Preface: Temperature extremes are stressing wildlife populations. I happen to be an advocate...

In the textbook Electrochemical Systems by Newman and Alyea, Chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$\mu_i=RT\ln(\lambda_i)\tag1$$ where ##\lambda_i## is the absolute activity...

I only know T3 = 4•T1 I was able to calculate the T2 = Tb = T4 I built four equations: T2 = p2V1 / nR T4 = p1V2 / nR p1/T1 = p2/T2 V1/T2 = V2/4T1 I put them together and got T2 = 2T1 I can't figure out the temperatures of A and C. I tend to think Ta could equal Tc (then I would be able to...

My thermodynamics is rusty and my current endeavors demand me to wield it, so here we go: I need a good starting point and/or references to study physical systems in thermodynamic equilibrium. Any references which address the fluid mechanics perspective of said systems are welcome too. Let me...

Hi, Starting from dS in term of H and P, I'm trying to find ##(\frac{\partial H}{\partial P})_t## in term of ##P,V,T, \beta, \kappa, c_p##. Here what I did so far. ##ds = (\frac{\partial S}{\partial H})_p dH + (\frac{\partial S}{ \partial P})_H dP## ##ds = (\frac{\partial S}{\partial H})_p [...

Would you please explain how the laws of thermodynamics are related to one another? Are the laws entirely independent of one another? I can see only a connection between the zeroth law and the second law. Following is the quote from my previous thread. 1. Zeroth law: The zeroth law of...

Hi, I don't understand what does it mean that at equilibrium the proper thermodynamic potential of the system is minimized. For example on the book Herbert B. Callen - Thermodynamics and an Introduction to Thermostatistics it is written: Helmholtz Potential Minimum Principle. The equilibrium...

I was reading about thermodynamics in my textbook wheni came across the following thermodynamics constants: However, i don't understand why did we define 1/V inthe constants. What is the point in doing this?

During a thermodynamic cycle, an ideal thermal machine absorbs heat Q2 > 0 from a hot source and uses it to perform Work W > 0, giving a cold source a heat Q1 < 0 with an efficiency of 20% . How much is the work done as a function of Q1 ?I have 2 question regarding this problem: 1) Why is Q1 the...

(a) We first find that: ##T_A=\frac{P_A V_A}{nR}=\frac{1\cdot 10^5 \cdot 4}{40\cdot 8.314}K\approx 1202.7904 K##, ##\frac{T_B}{T_A}=\frac{\frac{P_B V_B}{nR}}{\frac{P_A V_A}{nR}}=\frac{P_B V_B}{P_A V_A}=\frac{P_A \frac{V_A}{2}}{P_A V_A}=\frac{1}{2}##, ##\frac{T_C}{T_B}=\frac{P_C...

Hey, I have a question about the meaning of a variable in the Clausius-Clapeyron formula. My textbook (Daniel v. Schroeder) says that the Clausius-Clapeyron formula is (for phase boundary between liquid and gas) \frac{dP}{dT} = \frac{L}{T\left(V_{g} - V_{l} \right)} . What is V_{l} or V_{g}...

I have a question about the Thermodynamic Identity. The Thermodynamic Identity is given by dU = TdS - PdV + \mu dN . We assume that the volume V and that the number of particles N is constant. Thus the Thermodynamic Identity becomes dU = TdS . Assume that we add heat to the system (we see that...

What is the difference between thermodynamic and mechanical work? Should they show equal values in an experiment? If yes, what possible errors could cause if there is a difference in their values?

Im trying to find an advanced thermodynamic equation for a vacuum flask. I am looking for an equation to find the temperature of a liquid at time t as it cools down. Ignore the cap and bottom section; assume there is no heat loss in those areas. I'm just interested in the cylindrical...

Let me start out by saying it's been a LONG time since I've touched any thermodynamics but I'm starting to think that the answer for all 3 parts are the exact same (at least for work) Namely ##W = \int_{\frac{L^3}{2}}^{L^3} P(V) \, dV = NkT_0 \int_{\frac{L^3}{2}}^{L^3} \frac{1}{V} \, dV =...

Hi, I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space. To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the...

Hi, a basic doubt about thermodynamic functions and state variables. Take for instance transformations I and II in the following ##(p,V)## plane. As far as I can tell, just because the transformations are drawn as continuous lines they are reversible by definition. Namely we can transform...

Hi Folks, I promise there is an actual question at the end of this note. I couldn't see where to attach images on this forum page, so here is a link to a rough illustration and a photo of the project site in progress (the cabinet for the digester is partially built)...

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...

Very early in the development of thermodynamics, it was realized that the 2nd Law of Thermodynamics is not a law fundamental to the fabric of our cosmos, but only becomes true in the limit of the number of particles. It was none other than Boltzmann himself who realized and articulated this...

In AB, dU=0 (Isothermal) Hence dQ=dW W1= RT ln(2V/V) = RT ln(2) = 800R*ln(2) Q1=W1 = 800R*ln(2) Q2= Cp(300-800)=-500Cp = -500*2.5R Q3 = Cv(800-300) = 500Cv = 500*1.5R So Q= 800R*ln(2) -500*2.5R + 500*1.5R = 800R*ln(2) -500R Hence net heat absorbed is 800R*ln(2) -500R But. Suppose I find...

I post the working in the attached file

##(\frac {∂p} {∂ρ})_s=ϒ(\frac {∂p} {∂ρ})_T## The variables are p for pressure, ρ for specific mass density and γ is ratio of specific heats. I am able to show that the relation is valid for a perfect gas but cannot show its validity in general. The closest I get is ##dp=(\frac {∂p} {∂ρ})_s...

Hi gentlemen I want to know the classification of thermodynamic processes according to which is higher than which in work done during either compression or expansion. Thermodynamic processes like isentropic and isobaric. Thanks

I know that when it is ΔG>0 , it means there is no spontaneity, when ΔG=0 there is equilibrium, and when ΔG<0, there is spontaneity. But what happens when this is in the context of partial molar properties, when G is molar? I suppose molar ΔG is referred to a solution. Right? In that case, is...

I have managed to find the gamma value using the following equation: (T2/T1)= (P2/P1)(gamma-1/gamma. This will give me the answer of 1.29 SF. After this step, I am clueless. Can someone help me with this question please? I assume we have to find the enthalpy at state 1 to do that question.

A cylinder contains an initial volume V1 = 1m^^3 of a perfect gas at initial pressure p1 = 1 bar, confined by a piston that is held in place by a spring. The gas is heated until its volume is doubled and the final pressure is 5 bar. Assuming that the mass of the piston is negligible and that the...

The conclusion of my attempt I am listing below is that there do exist entropies for both but I am not sure. $$dU=TdS-pdV$$ $$dS=\frac{dU}{T}+\frac{p}{T}dV$$ Therefore, gas A: $$S=\frac{{\Delta}U}{T}+\alpha_A(\frac{-N}{{\Delta}V})$$ Gas B...

I read an article in Science Daily 'Physicists build circuit that generates clean, limitless power from graphene'. Can someone explain how to take this from the physics science experiment to the engineering prototype and implementation stage? Is this technology going to revolutionize the mobile...

After crossing out all the variables which I think equals 0 in the equation, I was left with: ∆PE + ∆U = Qin mg (0.2) + ∆U = 300 10*9.81*0.2 - 300 = - ∆U = -280J This was the answer I derived. However, the correct answer was supposed to be 123.3J. Please can someone explain to me how to get...

I realize that nothing causes an excited atom to emit a photon, and that it's a random process. But someone was asking me about why energized systems in general tend to lose their energy to the environment and move toward equilibrium. I mentioned that an inflated balloon, given a hole, will tend...

So the Legendre transforms are straightforward; define ##S_1=S-\beta E## and ##S_2= S-\beta E + \beta \mu n## then we get: ##dS_1 = -Ed\beta - \beta \mu dn + \beta PdV## ##dS_2 = -Ed\beta + nd(\beta \mu) + \beta PdV## And so by applying the equality of mixed partials of ##S_1## and ##S_2## we...

I was just wondering what is wrong with the following logic; From the Gibbs-Duhem relation we get, ##\frac{\partial \mu}{\partial P}\Big\rvert_T = v## Now consider, ##\frac{\partial v}{\partial \mu}\Big\rvert_T = \frac{\partial }{\partial \mu}\Big (\frac{\partial \mu}{\partial P}\Big\rvert_T...

#Can somebody please explain what is the difference between single phase and homogeneous phase in context with thermodynamics? #Also in the fundamental relations in thermodynamics like dg=vdp-sdT , it says this is applicable to homogeneous phase of constant composition. Isn't this equation...

We need to find the system's entropy variation. I don't think i understood pretty well what is happening in this process, can someone help me how to start?

So we know that every reversible engine working between the same temperatures will have the same efficiency(the same as Carnot engine). So let's consider for example reversible Otto cycle. So as you can see on the picture it is operating between ##T_1## and ##T_3##, so I was thinking that it...

Calculate the boiling temperature of methanol at 60 atm knowing that Tc = 513K, Pc = 78 atm and the acentricity is 0.555. I would like you to help me start the exercise. I thought about using the Pitzer Correlation to be able to calculate the fugacity coefficient, but I don't have the...

1. Adiabatic compression (When compressed quickly, there is no heat flow to the environment Q=0) Isochoric with heat loss (The syringe is still compressed, there should be no change in volume) Adiabatic expansion (When the syringe is released, there is work done only) Isochoric with heat gain...

Disclaimer: I am not a mathematician, I am a physicist. The thermodynamic identity is usually expressed in the following differential form $$ dU = TdS - PdV + \mu dN, $$ where U , T , S , P , V , \mu and N are the internal energy, temperature, entropy, pressure, volume, chemical...

I'm trying to delve into the reason why this is so. It seems that there are 5 fundamental properties: P - Pressure V - Volume (specific) T - Temperature S - Entropy (specific) U - Internal Energy (Yes, there are other types of energy, but they are fully determinable from these 5 - e.g...

Just to clarify, I'm aware of the two equivalent expressions of the first law ##\Delta U = Q + W## and ##\Delta U = Q - W## when applied to a certain system, though my question is primarily about ##Q## - for which, as far as I am aware, the convention is almost universally that ##Q > 0## if heat...

I'm in a first-year grad course on statistical mechanics and something about multivariable functions that has confused me since undergrad keeps popping up, mostly in the context of thermodynamics. Any insight would be much appreciated! This is a general question, but as an example imagine...

I don't understand how to use output from an NPT molecular dynamics simulation to compute a thermodynamic derivative. I need to compute this (where "d" is a partial derivative, "T" is a subscript that means, "at constant temperature," and "E" is internal energy): -(dE/dV)T I have a simulation...

I need to find the properties such as specific heat capacity, thermal conductivity, density and others.