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 reason about Gibbs energy change due to entropy not enthalpy?

    Before we prove this, consider a thought experiment. We have the following setup We break the left partition so that the gases on the left mix. What happens next is that due to a chemical potential difference, gas flows from the right compartment to the mixture. Note that - the partial...
  2. joejoe121

    A 50 cubic foot tank contains saturated 134a at 100F and a quality of 50%

    I've attached all my work and data table I used to answer the questions but there isn't an answer key so I would like a second opinion. a) The initial specific internal energy is.......Btu/lbm b) The initial mass is....lbm c)The average enthalpy of the withdrawn vapor is.....Btu/lbm d)The final...
  3. D

    A Black hole thermodynamics and accelerated expansion

    I have been thinking this for quite a few time. At this point we know that our universe is going through an accelerated expansion phase. I was also doing some work on blackhole thermodynamics, specially P-V criticality, heat capacity, Joule Thomson expansion, heat engine etc. These...
  4. T

    Heat Transfer Problem for Titanium Capsule

    Hello, all, I am currently trying to solve a problem at my internship concerning the heat transfer analysis of a Grade-2 titanium rod. The Ti rod is placed in an environment of 300 degrees C, and I am trying to solve the problem of the steady-state temperature of the Ti capsule. The length of...
  5. lost captain

    I Why pressure stays the same when doubling both volume and temperature?

    In thermodynamics we tend to think of pressure as the frequency of collisions with the walls of the container. And we say that the more the collisions the higher the pressure, the less the collisions the lower the pressure. So lets say we have an ideal monoatomic gas enclosed in a cube...
  6. M

    First Law of Thermo: Audience body heat warming a concert hall

    My approach to the problem was to try using Q = cmΔt by rearranging it to solve for Δt=Q/cm. Since the power per person is 70 W, there are 1800 people in the concert hall, and the problem asks for the temperature rise over two hours, I multiplied 70 W×1800 people × (3600 sec × 2) which gave me...
  7. LightPhoton

    I Volume of momentum space of an ideal gas

    In *An Introduction to Thermal Physics* by Schroeder, while deriving the multiplicity of an ideal gas makes the following statements (image below): Even in quantum mechanics, the number of allowed wavefunctions is infinite. But the number of independent wavefunctions (in a technical sense...
  8. L

    I First law of thermodynamics -- two different expressions for dQ

    Okay, so the first law ##dU=dQ+dW##. We all know that ##dU=C_VdT##. So that means that we have: $$dQ=C_VdT+PdV$$ Now I have a problem. We also have that $$dU=\left(\frac{\partial U}{\partial V}\right)_TdV+\left(\frac{\partial U}{\partial T}\right)_VdT$$ and substituting that in to ##dQ=dU+dW##...
  9. fluidistic

    I A paradox about energy balance and steady state

    I met a paradox I am unable to resolve. Here it goes: a special material is placed in thermal contact with 2 reservoirs kept at different temperature. The boundaries of the material that aren't in contact with the reservoirs are thermally insulated. The material being special is able to generate...
  10. L

    Issue deriving the third law of thermodynamics

    Okay, so we have that $$dU = \left( \frac{\partial U}{\partial V} \right)_S dV + \left( \frac{\partial U}{\partial S} \right)_V dS$$ And comparing that to the first law, we get that $$T=\left(\frac{\partial U}{\partial S}\right)_V$$. Comparing expressions of ##T##...
  11. U

    Physics, energy and sustainability research

    I'm 64. My background prior to 2001 - Aviation, experimental aircraft and aerodynamics, robotics, mechanical and software engineering, disaster recovery. Since 2001 - Human sustainability and global recovery, researching every related sector in depth in order to understand what can now be proven...
  12. heyhey281

    Additivity of thermodynamic potentials?

    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?
  13. L

    Clausius' Theorem and Entropy

    Okay, I agree with this logic. However, if we consider a reversible section first, then an irreversible section, I get the following: $$\frac{dQ_{rev}}{T} \leq \frac{dQ}{T} $$ which is the opposite to equation (14.8). Why is this? Is it "somehow" not viable to think of a reversible section than...
  14. L

    Thermodynamics of a Heat Engine - (First/Second Law)

    and the solutions: I am not sure why two of the bodies are at the same temperature to end with. I am pretty certain that they don't have to be - but the author of the problem set it this way for some reason I'm missing (my guess). My reasoning: Put 100 K and 300 K together for a short time...
  15. heyhey281

    B Quasistatic condition for a process involving a piston in a cylinder

    The time scale on which the change (such as a change in external parameters or a external parameters or an addition of heat) takes place is referred to as τ_exp. The relaxation time τ_relax, on the other hand, is the time that the system needs to return to a state of equilibrium after a sudden...
  16. E

    I Scaling Cake Baking Times

    I have a recipe that was a scratch cake of my grandmothers, but it is made for a ## 9 ~\text{in} \times 13 ~\text{in} ## baking pan. I wish to bake three ## 9 ~\text{in} ## rounds from the recipe. I can look up baking times online for the size, but times are dependent somewhat on the recipe...
  17. L

    Thermodynamics: Violating Clausius => Violating Kelvin

    I am not convinced that the heat entering ##T_l## from ##T_h## is equal to ##Q_l## in the Carnot engine. Why should it be? thanks
  18. heyhey281

    Thermodynamics: Two gases in a container

    Ideal gas: If the gases are of different type, I would say the entropy stays the same. The total entropy is in both cases just the sum S = S1 + S2, where S1 is the entropy of the first gas and S2 the entropy of the second gas. If the gases are of the same type, I think the entropy change is also...
  19. heyhey281

    B Why are the relative fluctuations of intensive properties so small?

    I get that the relative fluctuations of extensive properties (in thermodynamics) are tiny because you can divide the whole system in many subsystems and apply the central limit theorem, but I just dont get it with intensive properties. Could someone explain?
  20. 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...
  21. 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.
  22. 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...
  23. 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...
  24. 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...
  25. bucky3052

    A Resistance Force on Gas in Magnetohydrodynamic Generator

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  26. 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...
  27. 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...
  28. 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 =>...
  29. 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...
  30. 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...
  31. 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*}...
  32. 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 $$\delta q=0\tag{1}$$ $$\delta w=-P_2dV\tag{2}$$ $$dU=C_VdT\tag{3}$$ $$dU=-P_2dV\tag{4}$$...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. 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...
  38. 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 $$dS=\frac{dU}{dT}+\frac{pdV}{T}\tag{2}$$...
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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]
  45. 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...
  46. 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...
  47. 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...
  48. 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...
  49. 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.
  50. 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...
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