Thermodynamics Definition and 1000 Threads

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.
Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854 which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."
The initial application of thermodynamics to mechanical heat engines was quickly extended to the study of chemical compounds and chemical reactions. Chemical thermodynamics studies the nature of the role of entropy in the process of chemical reactions and has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged. Statistical thermodynamics, or statistical mechanics, concerns itself with statistical predictions of the collective motion of particles from their microscopic behavior. In 1909, Constantin Carathéodory presented a purely mathematical approach in an axiomatic formulation, a description often referred to as geometrical thermodynamics.

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  1. Z

    Chemistry How to understand the zeroth law through these specific equations?

    I've seen this math also in a lecture once. It seems very vague to me. Here is the relevant part of the book ##F_1## and ##F_2## are introduced as seen above. There is, as far as I can tell, no previous mention of them. Why does ##F_1(P_A,V_A,P_B,V_B)=0## signify thermal equilibrium...
  2. B

    Aircraft design fan

    I study Aerodynamics & Thermodynamics for my own pleasure, and am especially devoting my time now to civil aircraft design, in all its forms. I mainly learned from John Anderson and Jack Mattingly wonderful books. Thank you.
  3. L

    Confusion about work done by a gas - Thermodynamics

    This is chemistry but it's basically physics :D. I used PV = nRT, I get V = 37.44 L. This is fine. So then I have W = P(Vfinal - Vinitial). Vinitial is zero, because there was no hydrogen gas initially. So I get 3.78 kJ. And as the gas expanded from 0 L to 37.44 L, the gas has done positive...
  4. Antarres

    A Zeroth law of black hole thermodynamics

    I was looking at the proof of zeroth law of thermodynamics from the original paper by Bardeen, Carter, Hawking, which can be found here. Now, we have the Killing vector which is the generator of the horizon, we call it ##l^\mu##, and auxiliary null vector field ##n^\mu##, which we define to be...
  5. runinfang

    Thermodynamics: Possible process between a van der Waals gas and an ideal gas

    Since the energy variation is zero: $$ \Delta U = \Delta U_{1} + \Delta U_{2} = 0 $$ The energy for a monatomic ideal gas is ## u = CRT##, and the energy for a Van der Waals gas is $$ u = CRT - \frac{a}{v}, $$ obtained through $$ \frac{1}{T} = \frac{CR}{a + \frac{a}{v}}. $$ Summing the...
  6. bucky3052

    A Resistance Force on Gas in Magnetohydrodynamic Generator

    I am attempting to derive equations of state for a flow loop that incorporates a magnetohydrodynamic (MHD) generator to extract energy from the working fluid, an ionized gas. I have been able to find the following equation to define the power output of the generator: (where K is load factor, σ...
  7. Z

    Chemistry For irreversible process from state 1 to 2, why can the system not be isolated for reversible process from 1 to 2?

    Then $$q_{irrev}=0\tag{1}$$ Take the system from state 2 back to state 1 using a reversible process B. My first question is: why can the system not be isolated for this reversible process to be possible? Assume we have a non-isolated system in process B. Process A and process B together...
  8. Ignorantsmith12

    B Is it possible to apply thermodynamics to magnetic/weak/nuclear fields

    When I was taught about temperature in high school, I was told that substances that are hot have molecules that move fast, while substances that are cold have molecules that move slowly. I was also told that everything moves towards greater disorder or entropy. This is apparently because there...
  9. danut

    Ratio of volumes in a vertical cylinder with a piston

    First, I thought of the forces which are acting upon the piston. F1 + G = F2, where F1 = p1 * S and F2 = p2 * S p1 + mg/S = p2 I figured that before and after the gas' temperature rises, the piston has to be at equilibrium, so p2 - p1 = p2' - p1'. p1V1 = niu * R * T1 p2V2 = niu * R * T1 =>...
  10. LightPhoton

    How to turn partition sum into an integral?

    In, *An Introduction to Thermal Physics, page 235*, Schroder wants to evaluate the partition function $$Z_{tot}=\sum_0^\infty (2j+1)e^{-j(j+1)\epsilon/kT}$$ in the limit that $kT\gg\epsilon$, thus he writes $$Z_{tot}\approx\int_0^\infty (2j+1)e^{-j(j+1)\epsilon/kT}\,dj$$ But how is this...
  11. Z

    Chemistry Is the differential of heat in a reversible process in an isolated system equal to zero?

    If a process is irreversible, on the other hand, then $$\oint \frac{\delta q}{T}\leq 0=\oint dS\tag{1}$$ Apparently, from this equation we can conclude that $$dS \geq \frac{\delta q}{T}\tag{2}$$ How do we mathematically justify the step from (1) to (2)? Next, consider an isolated system...
  12. domephilis

    Change in Entropy When Mixing Water at Different Temperatures

    After re-reading the book, I did figure out what I was supposed to do. Take both waters through a series of reservoirs to bring them down to their final temperature while allowing for a quasi-static process. Thus, $$\Delta S = m_1c \int_{T_1}^{T*} \frac{dT}{T} + m_2c \int_{T_2}^{T*}...
  13. Z

    Chemistry A few questions on an irreversible adiabatic expansion of an ideal gas

    When we remove the stoppers, the gas expands and the piston shoots up and eventually reaches a new final position in which the internal and external pressures are the same. Apparently we can write $$\delta q=0\tag{1}$$ $$\delta w=-P_2dV\tag{2}$$ $$dU=C_VdT\tag{3}$$ $$dU=-P_2dV\tag{4}$$...
  14. Z

    Chemistry How to derive 2nd law extremum principles for U, A, G, and H?

    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...
  15. Z

    Chemistry Entropy in isolated composite system for irreversible process

    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...
  16. Z

    Chemistry No heat exchange with the surroundings in an irreversible expansion of an ideal gas?

    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...
  17. Z

    Chemistry Understanding thermodynamics of a stretched rubber band

    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...
  18. Z

    Chemistry Show that book levitation by absorption of heat violates 2nd law

    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...
  19. Z

    Chemistry Why can we differentiate this entropy total derivative with repect to Temperature?

    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 $$dS=\frac{dU}{dT}+\frac{pdV}{T}\tag{2}$$...
  20. Z

    Chemistry Two approaches to calculating entropy differ by factor of two. Why?

    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...
  21. S

    B Can energy be stored in a single particle indefinitely?

    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...
  22. askingask

    Vacuum by condensation causes water to boil?

    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...
  23. D

    Help on My IB Extended Essay--Finding a data set for Redshift

    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...
  24. R

    Power Radiated From a Copper Cube

    ##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...
  25. walterminator

    Thermodynamics: Cooling of a heated block of iron in contact with air

    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]
  26. imdesperate

    Closed cycle of an ideal gas

    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...
  27. S

    I Questions about Hawking radiation and extremal black holes...?

    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...
  28. D

    Classical Looking for a thermodynamics book that 'ties it all together'

    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...
  29. S

    I Vacuum up-tunneling with high-energy events?

    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...
  30. cheetah

    Engineering How Do You Calculate Values Using pV Diagrams for a Monatomic Gas?

    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.
  31. tellmesomething

    Chemistry Graph of several thermodynamic processes

    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...
  32. Omega0

    B Why Does Black Hole Entropy and Information Loss Matter?

    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...
  33. Chestermiller

    I Interesting Thermodynamics Problem deleted in PhysicsStackExchange

    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...
  34. G

    Internal energy won't add up to 0 in cyclic process

    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. $$ΔU_{AB} = ΔU_{isothermal} = 0$$...
  35. J

    I Trying to wrap my head around gas turbine thermodynamics

    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...
  36. MatinSAR

    Question about the thermodynamic temperature scale

    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 :$$dQ=Pdv$$
  37. MatinSAR

    I Work done in cycle of a refrigerator (in Heat and Thermodynamics by Zemansky)

    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?
  38. J

    Errors in Experiment with Low and High Conductivity Materials

    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...
  39. Yseult

    I Questions about my Understanding of Thermodynamics and Statistical Mechanics

    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...
  40. aladinlamp

    I Adiabatic cooling in this process involving liquid ammonia

    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...
  41. D

    Thermo Final Review - specific heat for ideal gas

    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?
  42. MatinSAR

    Recommendation for project related to thermodynamics

    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...
  43. Q

    B Are wind farms stealing the cooling capacity of the wind?

    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...
  44. cianfa72

    I State equations for a thermodynamic substance/system

    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.
  45. E

    Does Heating a Metal Wire Change Its Properties?

    I have attached a PDF file.
  46. Karfen

    Is the Molar Specific Heat of Air Similar to Hydrogen?

    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?
  47. Z

    I Graphical difference between adiabatic and isothermal processes.

    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 $$dU=\left (\frac{\partial U}{\partial T} \right )_VdT + \left (\frac{\partial U}{\partial V} \right )_T dV\tag{2}$$...
  48. Z

    I Why does an ideal gas satisfy ##(\partial U/\partial P)_T=0##?

    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?
  49. Z

    I Where are the limits being taken in these thermodynamics equations?

    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...
  50. Z

    I How to measure average thermal conductivity of a metallic material?

    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...
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