Thermodynamics Definition and 1000 Threads

My question emerges from my desire to calculate the optical depth, which should be unitless, for an inhomgeneous cloud of radius ##r##. For a homogeneous medium, the optical depth can be defined in terms of the density of a cloud relative to the density of the condensed medium: $$\tau = \alpha...

Thermodynamics deal with quantum mechanics all the time, so I wondered what role it played in a internal combustion engine. Could we calculate it and how does it affect the engine's final output?

In his Chapter 13.3 (2nd edition), Callen gives the standard form for the virial expansion for the mechanical equation of state of a fluid as an exapnsion in powers of the molar volume ##v##: $$P = \frac{RT}{v}\left(1 + \frac{B(T)}{v} + \frac{C(T)}{v^2} + \dots \right) \equiv P_{ideal} +...

Callen asks us (with respect to an ideal gas) I had thought to proceed as follow. We have the definition for the singular reaction: $$\ln K_s(T) = - \sum_j \nu_j \phi_j(T).$$ Now a reaction which is the sum of this reaction with itself (doubled reaction) has ##\nu_j \to 2\nu_j## so that its...

In Ch. 13.1 of the second edition, Callen defines a general ideal gas as follows: Of course, all of these can be proved as a theorem of statistical mechanics given a no-interaction assumption. At any rate, my claim is about Callen's claim that a single component ##j## of general ideal gas...

In Chapter 13.2 of his text, Callen states that the chemical potential with respect to the ##j##th component of an ideal gas can be written as $$\mu_j = RT \left[\phi_j(T) + \ln P + \ln x_j \right].$$ He states this outright and doesn't prove it, and I am trying to do so now. Based on what has...

In writing up a paper on some research work on the effects of transients on Lithium Iron Phosphate batteries, I am laying out the thermodynamics and energetics for the reaction laid out below, but am having trouble finding the numbers for the reaction. Does anyone know the correct figures to...

A standard 12 gram cartridge contains both liquid and gaseous CO2 at 850psi. Assuming we are venting to atmosphere at sea level, how much energy can be extracted from the cartridge? We know it will expand to 12 grams * 22.4 liters/ 1 mole (44grams) = 6.1 liters. But how much energy did...

Callen asks us the following question in his famous textbook: I have answered as follows: However, I get the wrong answer and, in fact, the correct answer obtains from using ##\Delta P = -\rho_s g h##; that is, using the solid density for the change in pressure. Now why on earth should this...

Consider a system which is characterized by the extensive variables ##(U,V,N_1,...,N_m)##. For a quasistatic process which occurs in contact with some pressure reservoir and where the ##N_i## are constant, one has $$dU = TdS -PdV \implies TdS = dQ,$$ where the implication follows from the First...

In a discussion about the (change in the) Helmholtz potential being interpretable as the maximum available amount of work for a system in contact with a thermal reservoir (i.e. the free energy), Callen seems to insist this fact is true only for reversible processes. Why should this be? I...

I know process B absorbs heat but I can't determine the heat of process A. In adiabatic process, Q = 0 but process A is not adiabatic. I only know both W and ΔU will be negative for process A but how to know Q? Thanks

Some evidence (Bekenstein, Hawking, Jacobson, Verlinde, ...) points to the idea that gravity is really a thermodynamic theory in disguise. Other evidence (Susskind, Maldacena, Witten, ...) points to the idea that gravity is dual to a lower dimensional conformal field theory (CFT). Are these two...

I was checking bait cannons and potato guns on the internet because they are fun. Maybe one day I'll build my own. First of all, these cannons use multiple sources of energy (combustion using hair spray, dry ice, etc.). I'll just consider compressed air cannons because I think they are the most...

Hi all, I've started working recently in a new job as an engineer in a lab with a bunch of physicists. A job they've given me is to size a water/glycol chiller (and basically design the hydraulic system i.e. fittings, tubing etc) to cool a bunch of equipment they've got in a few insulated...

Hello I was checking the book THERMODYNAMICS AN ENGINEERING APPROACH (the 2023 version) because I saw it recommended on the internet. I was surprised to find an error in one of their examples because it is already on the 10th edition. I'm pretty sure about the error but I wanted to confirm it...

I was trying to learn physics from a coaching institute and they started optics before they started Electricity and Magnetism and the lecturer went on saying somethings which I didn't completely understand. Is the coaching institute doing it wrong teaching me Optics before they taught me...

Energy lost by water = Energy gained by ice Energy lost by water = 0.16 x 4200 x (100-t) Energy gained by ice = 0.205 x L + 0.205 x (t) (where t is the temperature at thermal equilibrium). However, there does not appear to be enough info to continue. The solution, however, considered t to be...

I want to work out how to calculate the pressure change in a gas cylinder if it is used to fill another cylinder to a lower pressure. For example, if a 50 litre gas cylinder initially at 200 bara is used to fill a 600 litre cylinder from atmospheric pressure to 1.5 Bara. What would the change...

Obviously, we know intuitively what they mean, but it seems that physicists have developed an objective definition for all of these. If I were to guess, I'd say that: - a gas is vastly less compressible than a liquid or solid (i.e., which are considered in thermodynamics as basically...

TL;DR Summary: I'm trying to understand what research fields I would have access to as a person who's majoring in chemistry. So how deep does thermodynamics go and how much of a foothold could I get into research on it as someone who's majoring in chemistry? Or is it really only accessible to...

I suppose it means that the gadolinium melts only at one particular location, but I have no idea how to take it mathematically. Could I just say that local melting is when I destroy a bond between two gadolinium atoms? Could I calculate with this? I just need to understand what I am supposed to...

To be honest, thermodynamics is really not my strong suit and I get confused when and how to apply formulas. My thought process is as follows: - there are two ideal gases (ideal gas law applies) - the pressure remains constant (isobaric process), so p1= p2 = p - I imagine there being two...

Hi guys, Can you give me some feedback on whether my calculation is correct? I applied the formula below (Boltzmann Distribution) but I didn‘t know what to use for the variable z. I don‘t even know if I used the correct equation. Can you help me further? The task is: Consider a system of...

Assume that a closed system of cylindar filled with ideal gas consists of a movable piston.We know from the 1st law dQ=dU +dW. According to the 2nd law mechanical energy can be totally converted into heat energy but heat energy cannot be converted completely into mechanical energy.The question...

Hello, is someone able to explain why these two are wrong. I am not sure how to figure out the enthalpy direction as the reaction is not changing state of matter, nor is it changing temperature. (Please solve without calculating anything) Thank you

I don't understand, can you calculate efficiency only using the temperature?

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...

For this problem, The solution is, ## Q = 54500 J ## , however, since the calculation for heat uses the first law which involves ##5 \times 10^{-3) m^3 ## value for the initial volume, should the finial answer not be to 1 sig fig as well? This would give ## 60000 J ##. Many thanks!

For part(a) of this problem, The solution is, a. 160 J In part (a), are they referring to the simi-circular path from R to S instead of the path from R back to R? I though the closed path would be the path from R to R, or the path from S to S, where both give W = 0 since ##W = P(V_f - V_i) =...

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: $$ \mu_i = RTln(\lambda_i) \tag {1} $$ where ##\lambda_i## is the absolute...

TL;DR Summary: Struggling to structure the problem and derive an analytical solution for gas expanding into other gas in a rigid tank. Preferred formulation is fixed control volumes. This is not a homework problem. The problem: Two control volumes (A and B) are in a rigid tank filled with air...

Hello, I want to model a thermal battery based on phase change materials (PCM). It is a plate heat exchanger immersed in a PCM bath. The diagram is given in the attached file. I want to determine the temperature at each moment and from everywhere in the battery. The hypotheses are the...

The answer given for part (c) in the back is that temperature doesn't change as the gas in cylinder A expands to fill cylinder B. The thermodynamic system here is composed of the two cylinders A and B joined by some pipe. But, I cannot find a satisfactory explanation for temperature...

Hello, Could someone please help me understand how to approximate how long it will take for liquid nitrogen in a room temperature container to completely evaporate. Here's the scenario: I have a metal container (41x13x15") filled with 5.5" of liquid nitrogen (just released from a Dewar ~ 320F)...

Concerning cosmological structures (like galaxies, clusters of galaxies, gas bodies, superclusters...etc) if the elements that make them are close enough they will be attracted towards each other by gravity. Contrarily, if they are sufficiently far apart they will get further away following the...

Hey! Does anyone have the large/full description of Maxwell's demon thought experiment? I've read it on Wikipedia, but I was wondering if someone knows a better source I can reach legally. Thanks.

In the thermodynamics textbook there is written: 𝛿𝐴 = 𝑇𝑑𝑆 − 𝑑𝑈 = 𝑑(𝑇𝑆) − 𝑆𝑑𝑇 − 𝑑𝑈 = −𝑑(𝑈 − 𝑇𝑆) − 𝑆𝑑𝑇 = −𝑑𝐹 − 𝑆𝑑𝑇 How did we get the bolded area from TdS? Is that property of derivative, integral, or something else :/

So I'm reading through Cengel's thermodynamics textbook, and came across this solved example: Firstly, pressure in this context I'm assuming is vapour pressure? Since we're dealing with pure substances in this chapter. But what's confusing me is, here's the diagram I have: They've not...

I have some doubts about a thermodynamics exercise I did-I'll write down the text and show how I tried to solve it to see if I reasoned it out right. In a container of thermal capacity ##C## containing ##1.0 kg## of ice at a temperature of ##-4.0 °C##, a mass of ##3.0 kg## of water is poured...

I work as part of the engineering team running an incinerator. When the ash is removed from our furnace, it creates an open system between the furnace (which is close to being a vacuum) and the atmosphere. For many reasons, this is not ideal. We are looking to add a second door to this ash...

Hi everyone, I'm in a graduate level mechanical engineering thermodynamics class. We're working on derivative reductions using the gibbs and maxwell relations. I was wondering if anyone has any good sources of practice problems that I could use. I've looked through my textbook and there are...

I found this article* about the behavior of quasar outflows in cosmology and how they can create a magnetic field. In section 2.1.4., the authors say that when a quasar produces a "wave" or an outflow, the material will be emitted with energy coming from both the quasar itself and the Hubble...

https://en.m.wikipedia.org/wiki/Heat_death_of_the_universe Is the heat death of the universe completely unavoidable in an universe with an accelerated expansion dominated by dark energy like ours? Or can there be any way to avoid it according to current knowledge, observations and experiments...

There has been much discussion about how could we (theoretically) extract energy from the accelerated expansion of the universe. However, the only gedankenexperiment I can found is the "tethered galaxies" one (e.g. https://arxiv.org/abs/astro-ph/0104349). However, has somebody proposed an...

I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales. At some part (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic...

I found a paper (https://arxiv.org/pdf/astro-ph/0411299.pdf) which talks about quantum systems emitting energy due to spacetime expansion. Is this true or only a hypothesis?

Can a train (e.g. like a maglev train) use a set of permanent magnets (not electromagnets) that somehow can be propelled and maintain at least a constant speed with them? Is this an example of such system...

I found an old article (https://journals.aps.org/pr/abstract/10.1103/PhysRev.137.B1379) which talks about conservation of energy in an expanding space. Apparently, the author found that energy is conserved at local scales (like the motion of planets in our solar system) as one would expect, but...