Thermodynamics Definition and 1000 Threads

For the internal energy function ##U(S,V,\{n_i\})## we have $$dU=TdS-pdV+\sum\limits_{i=1}^{N_s}\mu_id n_i\tag{1}$$ where ##N_s## is the number of species in the system. We also have $$dU=\delta q+\delta w\tag{2}$$ by the 1st law of thermodynamics. I am using ##\delta## to denote an inexact...

I am using the symbol ##\delta## in ##\delta q_{rev}## and ##\delta w## to denote an inexact differential. $$\delta q_{rev}=C_VdT+\frac{nRT}{V}dV$$ We can turn this inexact differential into an exact differential by multiplying by the integrating factor ##\frac{1}{T}##. $$\frac{\delta...

My doubts are about the second question above, ie the irreversibly expansion. For the first question, we have a) $$dS=\frac{dq_{rev}}{T}=\frac{nR}{V}dV$$ $$\implies \Delta S=nR\ln{\frac{V_2}{V_1}}=2.88\mathrm{\frac{J}{K}}$$ b) $$q_{rev}=T\Delta S=298.15\text{K}\cdot...

Consider the function ##U=U(T,L,N)##. $$dU=\left (\frac{\partial U}{\partial T}\right )_{L,N} dT+\left (\frac{\partial U}{\partial L}\right )_{T,N} dL+\left (\frac{\partial U}{\partial N}\right )_{T,L} dN$$ and define $$C_L\equiv\left (\frac{\partial U}{\partial T}\right )_{L,N}$$ By the...

Let's consider the book to be our system. The book spontaneously absorbs heat from the surroundings and somehow converts this to gravitational potential energy. Assuming gravitational potential energy is zero at the table top, the potential energy at ##3.2\text{cm}## above the table is...

Ignoring chemical potential for now, the natural variables of ##U## are ##S## and ##V##. Thus $$dU=\left (\frac{\partial U}{\partial S}\right )_VdS+\left (\frac{\partial U}{\partial V}\right )_SdV=TdS-pdV\tag{1}$$ which we can rewrite for ##dS## as $$dS=\frac{dU}{dT}+\frac{pdV}{T}\tag{2}$$...

Here is how I did this problem Let's call the two samples sample 1 and sample 2. The change in entropy for sample 1 is $$\Delta S_1=\int dS_1=\int_{U_1}^{U_1+\Delta U}\frac{1}{T_1}dU\tag{1}$$ $$=\frac{1}{T_1}\Delta U\tag{2}$$ Similarly, ##\Delta S_2=-\frac{1}{T_2}\Delta U##. Note that I...

Can energy be stored in a single particle without it being lost over time? I mean, photons would be an exampld in principle, but they get redshifted as the universe expands and become less energetic as time goes by We could store that energy in form of kinetic energy for individual...

So basically if I have a closed container with a valve, and inside the container there is water. Now i heat the container and boil the water. The valve is open so steam escapes form there. I now close the valve and cool the container causing the steam to condense inside. Inside the container is...

TL;DR Summary: Need help with finding a data set for redshift and suggestions on my topic. Hey. I am currently working on writing my IB (International Baccalaureate) Extended Essay (4000 word paper) with a focus on thermodynamics and astrophysics. So far the topic is using the increase in the...

##e## is emissivity ##\sigma## is the Stefan-Boltzmann constant, ##5.67*10^{-8} W m^{-2} K^{-4}## A is the surface area T is the temperature ##\frac{dQ}{dt}## is the rate of heat transfer or radiated power At first glance this appeared to be an easy problem, just plug in the values and go, so...

Φ = 𝜑S (dQ/dt) = k*S*dT avec dT = (1500 + 273.15) - (40 + 273.15) = 1460 [k] avec dQ = - 0.24 [kg] * 440 [j/(kg * k)] * 1460 [k] = - 154176 [j] donc, -(154176)/dt = 40 [W/(k * m²)] * 0.0062 [m²] * 1460 [k] = 362.08 [W]

Hello PF, this is my first time posting here. I will try my best to make my formulas readable. So I know what needed to be done: The efficiency is calculated by the formula: ##\eta = \frac{-A}{Q_+}## With ##A## being the total work done in the cycle, ##Q_+## being the heat absorbed in the...

I'm studying if there is some way to avoid black hole evaporation, even if it requires a very special set up of conditions... Theoretically, extremal black holes (both for rotating Kerr and Reissner-Nordström ones) would avoid evaporation as they would not emit Hawking radiation. Since...

I am currently a highschool student, and while I've learnt a bit about thermodynamics such as the first and second laws, their implications, I'd like to know how that stuff relates to gases and (without going too deep into it) phase change. Due to the structure of our curriculum, I've learnt...

I was reading these papers by Sean Carroll (https://arxiv.org/abs/1405.0298; https://arxiv.org/abs/1505.02780) in which, among other things, he argues against vacuum up-tunneling occurring in the universe. He only acknowledged that it would be possible in the first moments of the universe while...

I’m having trouble with a Thermodynamics Assignment and could use some help. I’ve been given the below graph and told to consider the processes shown for a monatomic gas. I’ve been asked to answer these questions with no further information besides the graph.

I graphed it similar to this My query is say if the last process wasn't mentioned, I.e the process from A TO D, would the state D have the same pressure as state A then? In thermodynamics for a reversible system we say that if it undergoes a change in pressure volume the exact pressure and...

We know that there is no law of conservation for the entropy. It is quite the contrary: If we have a closed system without exchange of heat the entropy cannot get less. It will reach the max. If we have not a closed system but a stream of entropy only into a system, the entropy will increase...

I came across this very interesting Thermodynamics problem in PhysicsStackExchange. It was deleted by the OP because the moderators, in their infinite wisdom, gave him a hard time about its being a homework problem which was, in their opinion, a "check my work" post, rather than a "I'm having...

My problem isn't exactly with calculating the actual changes in internal energy, I'll put those values below. My problem is that I can't get the values to add up to 0, and I don't understand why since for cyclic processes, by definition, ΔU must equal 0. $$ΔU_{AB} = ΔU_{isothermal} = 0$$...

I created a crayon drawing to aid the discussion below: Basically if you have a blower of low pressure, and you blow it through a tube which has a very hot center, when the heat is added to the air, does the pressure of the air increase after passing by the fire, or is that impossible since...

My first problem is to find the absored and rejected heat. Can I say that it is equal to the work done in an isothermal proccess (##dQ=Pdv##)? My reasoning : We have ##dQ=C_V d\theta + Pdv##. For constant temperature it becomes :$$dQ=Pdv$$

I guess the first one is wrong. Because in this cycle we have ##|Q_H| > |Q_L|## then ## |Q_L| - |Q_H| ## is negative and caanot be equal with ##|W|##. Am I right?

TL;DR Summary: Trying to understand why there might be errors when using certain materials in a physics lab and how aluminum foil might impact this. I am looking for assistance on answer these questions. 1) What would likely be a significant source of error in performing this experiment on...

Good afternoon all, I have two questions to check my understanding/understand better those questions. Why is heat capacity an important quantity in thermodynamics and statistical mechanics? From my understanding, heat capacity is an extensible property so any change in the system would result...

Entry conditions: liquid ammonia , 1 bar , temp -34 celsius, i supply heat Q to heat it to 4.5 celsius, 10 bar, than i release it into empty vessel until inside reaches also 1 bar, expansion,adiabatic cooling, uses internal energy of ammonia to expand and cool itself 1. can we assume, after...

TL;DR Summary: why is the answer "all of the above"? Could someone explain why the correct answer is all of the above? I understand that Cv implies a constant volume process, but what about the other two?

TL;DR Summary: I'm currently studying physics (undergrad level). I want to find a project related to thermodynamics to present it to my professor. I am reading this book: Heat and Thermodynamics: An Intermediate Textbook by Mark Zemansky and Richard Dittman...

Hi, this is a atmospheric physics question.When the sun heats up the ground (dark granite slab/asphalt), makes a thermal column of air rise, gradually accumulating into a higher pressure area, and then wind, when it moves from higher pressure to a lower pressure area, it is distributing the heat...

Hi, as follow up to this thread I believe for any substance/thermodynamic system there exists actually a set of 3 state equations between the 5 variables ##(U,T,S,p,V)##. For example in the case of ideal gas which are the 3 equations ? Thanks.

I have attached a PDF file.

And this is the Cv graph for hydrogen: I think the Cv graph for air is similar with this graph. But I don't know the answer, can someone tell me?

Let me first get through a few calculations to set up the main part of this question. From the first law, we have that $$dQ = dU - dW\tag{1}$$ Now, we also have $$dU=\left (\frac{\partial U}{\partial T} \right )_VdT + \left (\frac{\partial U}{\partial V} \right )_T dV\tag{2}$$...

The book I am reading says that by definition, the ideal gas satisfies the equations $$PV=nRT\tag{1}$$ $$\left (\frac{\partial U}{\partial P}\right )_T = 0\tag{2}$$ where does (2) come from? In other words, what justifies this equation in the definition above?

Here is a passage from a book I am reading My question is about the limits. Are all the limits in the derivation above done for ##P_{TP}\to 0##? In particular, is it ##\lim\limits_{P_{TP}\to 0} (Pv)## that appears above? The author omits this information in all but the first limit and it...

Heat conduction is the transport of energy between neighboring volume elements in a material as a result of the temperature difference between them. The "fundamental law of heat conduction", as it is called in the book I am reading, is a "generalization of the results of experiments on the...

Hi,I m studying for college and I need to receive some info from you guys. Which books should I use to study mechanics,thermodynamics,electricity and magnetism? I have no idea what books I should study because my own physics teacher has some pdfs in her USB and I can t borrow the USB because...

Hi, I have a question regarding the evolution of idea in the field of thermodynamics. Boltzmann is genereally credited with the notion of stasticis and it's relation to entropy. However, Boltzmann was inspired by the work of Maxwell (who himself followed the conceptual models of Bernoullli for...

In Halliday's physics book, there is an example of the first law of thermodynamics that shows its application. The figure below explains this example: Here is a question, if the element alone is chosen as the system, doubts arise in the first law, because in this system, Q<0 (because heat is...

Let's consider the system as both internal chambers together, ie everything inside the adiabatic walls. We have ##Q_{sys}=Q_{gas}+Q_{evac}=0## because we have adiabatic walls and ##W_{gas}+W_{evac}=0## because of the rigid walls. ##\Delta U = U_f-U_i=Q_{gas}+Q_{evac}+W_{gas}+W_{evac}=0##. How...

Consider the problem of measuring the heat capacities of solids using an electrical method where a resistance wire is wound around a cylindrical sample of the material. Why and how is the dissipated energy in the first case considered work and not simply an internal exchange of heat (which...

My question is about units. For the first part, we can solve the state equation for ##P## as a function of ##V## and ##T##. We obtain $$P(V,T)=\frac{RT}{V-b}-\frac{a}{V^2}\tag{1}$$ The units question already comes up here because as far as I can tell the right-hand side doesn't have the...

I dont have an solution Attempt. Maybe something with PV=nRT but this is for ideal gas and H2O is liquid. An other formula they introduced us to is: dE=-P*V

I am posting this question after I thought I had easily solved the problem, but then when I checked the back of the book I saw that I was incorrect. Here is what I did. (a) $$W=-\int_{V_i}^{V_f} PdV\tag{1}$$ $$V=V(P,T)-\frac{nRT}{P}\tag{2}$$ $$dV=\left ( \frac{\partial V}{\partial P}\right...

It seems to me that we can already answer b): if gas leaks from the high pressure container to the atmosphere, there is no expansion work. The container loses gas, which means in ##PV=nRT## we have ##n## going down and ##P## going down, and perhaps ##T## going down. But no work. As for a), I...

I'd like to show two different ways of defining work in a hydrostatic (PVT) system in a cylinder with a piston. One way is in a book that I have slowly come to hate: Physical Chemistry by Silbey, Alberty, and Bawendi. In that book, work is defined using the external pressure on the piston...

(a) (b) Here is a plot of this function T of R It seems that as the resistance goes up the temperature goes down. Not sure what to make of this physically speaking. My question is about the requested log-log graph. Above we have a function T of R, but we want a function ##\log{T}## of...

Here is the table As far as I can tell what we have here are four constant-volume thermometers (each column represents a thermometer). These thermometers work by having a certain constant volume of some specific gas in a bulb. We immerse the bulb in whatever temperature we would like to measure...

I posted another question about a thermodynamic system with three coordinates, namely, that of a metallic wire. We can describe that system with temperature, wire tension, and wire length. The result derived in that question was that the partial derivative of wire tension relative to absolute...