Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Maybe combine with [tag:statistical-mechanics].

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852 views

How do I derive the critical temperature for bose condensation in two dimensions?

In class we derived the 3D case, but there's a step I don't understand: $$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
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30 views

A micro-reversible stochastic process that models transitions between states with variable energies

Suppose we have a system with 3 possible states A, B and C (there could be $n$ states as well) with energies $E_a(t)$, $E_b(t)$ and $E_c(t)$ that vary with time. If our system has a constant finite ...
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16 views

Fermi-Pasta-Ulam for the beam equation

The Fermi-Pasta-Ulam numerical experiment is based upon the discrete wave equation, with a small non-linearity added to the forcing term. Does anybody know of similar research performed on the beam ...
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20 views

Constancy of Coefficients of Additive Integrals Throughout Subsystems of a Closed System

I'm studying Landau and Lifshitz's Statistical Physics, Part 1, 3rd edition and am looking for clarification on the following statement, which appears on page 11 in the section on The Significance of ...
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23 views

Ratio of Stagnation to Normal Flow Properties in Incompressible Flows

I know in compressible flows the ratio of stagnation to normal flow variables is a function of the Mach number and usually the specific heat ratio. Does this ratio mean anything for incompressible ...
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34 views

Volume Operator / volume phase-space-function in thermodynamics

In Thermodynamics, one often encounters the derivation of pressure as the generalised force that belongs to the extensive state-variable of the volume. Postulates: One looks just at a system of many ...
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42 views

Does entropy flatten spacetime?

Forgive me if this is a non-question, but I could not find anything regarding this. I only know parts of GR, and I am not familiar with the math. Since energy and matter density curve spacetime, ...
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16 views

Conduction shape factors - textbooks inconsistent

I'm working through a energy flow problem, and need to use the conduction shape factor for 'Row of N long cylinders against planar surface'. However two different texts give two different formulas for ...
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118 views

Why does the characteristic curve (V vs I) for a light bulb backbend?

When teaching Ohm's Law, I have students do an exploration of a small, incandescent light bulb with a low frequency (1-2 Hz) sine wave. It's a simple series circuit of source and light bulb, ...
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112 views

specific heat of water and ice

We know that denser objects have lower specific heat capacity. Since water is more dense than ice, water must have lower specific heat capacity than ice but we know that water's heat capacity is ...
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71 views

Partial derivatives of Internal energy

If we look at fundamental thermodynamic equation we see that $$dU=\left(\frac{\partial U}{\partial S}\right)dS+\left(\frac{\partial U}{\partial V}\right)dV.$$ We call $\left(\dfrac{\partial ...
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139 views

Otto and Carnot efficiency comparison

Lets say both engines operate between same temperature limits. Carnot eff: $$ e_\text{Carnot} = 1-\frac{T(L)}{T(H)} $$ Otto eff: $$ e_\text{Otto} = 1-\frac{T(4)-T(1)}{T(3)-T(2)} $$ ...
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109 views

The formula for calculating work transfer for a reversible adiabatic compression

Should we not be using Pdv for calculating the work done during a reversible adiabatic process ? Why are we using Vdp ? Can some one please explain this ? (P.S. I'm taking an introductory course on ...
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28 views

Lens-Mirror systems and conservation of specific intensity

This came out of a discussion I started yesterday and a related discussion I found. I'll recap the problem quickly: Consider two blackbodies, with surface areas $A_1$ and $A_2$ and temperatures $T_1$ ...
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49 views

Car Heating due to the sun: comparison of different contributions

Let's imagine that we need to choose a car in order to minimize the Temperature that the inner part of the car will reach after some hours under the sun. We know that two factors (if we suppose that ...
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77 views

Entropy Change for a Thermally Isolated System

Clausius' Theorem states that $\int\frac{dQ}{T}\leq0$ for a closed cycle, with equality for a reversible cycle. Suppose we wish to take our system around a closed cycle such that the path from A to B ...
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86 views

How to relate internal energy to atomic motion?

I am trying to conceptualize how atomic motion leads to the thermodynamically-defined internal energy (denoted as $U$ below) through some broad mathematical relationships. I get that the internal ...
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24 views

How do I calculate temperature diffusion in a gas contained in a heatsink?

To simplify the problem, consider a sphere with a diameter of $25\mathrm{mm}$ inside an infinite heatsink at $300\mathrm{K}$. At $t=0$ I instantaneously raise the temperature of the gas in the ...
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71 views

Is the diffusion coefficient time-dependent?

It is known that in the partial differential equation: $$u_t=au_{xx} $$ within the limits $0<x<1$ and $a>0$, the diffusion coefficient, arises in the mathematical modelling of a process of ...
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481 views

Molecular structure correction factor in Mass Flow Controller

This question concerns device called Mass Flow Controller (or Mass Flow Meter). For a video explaining the principle: see https://www.youtube.com/watch?v=G62ma2IFh9o These devices are factory ...
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194 views

Confusing Chemical potential of mixtures

I feel that there are very few textbook that treat the chemical potential of mixtures in an understandable clear way, which is why I wanted to ask here about certain things? Although I do not have a ...
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122 views

What does the net force do with this droplet in magnetic field?

Consider a spherical droplet with radious $R_d$ which is coated with an immiscible ferrofluid with volume equal to $2v_f$. While the droplet is in rest on a surface, if I approach two magnets in ...
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109 views

Validity of topological thermodynamics?

I've been reading some material by R. Kiehn, developing a topological approach to non-equilibrium thermodynamics through Cartan forms, where the fundamental claim is that irreversible processes are ...
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335 views

Diffusion in a chemical potential gradient

I am having troubles to understand to connection between equilibrium and non equilibrium thermodynamics. I am studying a mixture of molecules $A,B,C$ and solvent $S$. The free energy $F$ is given by ...
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62 views

Positivity of Bulk modulus and shear modulus in isotropic materials

I have been searching through many resources, but could not find a proper thermodynamic reasoning for why bulk and shear moduli for isotropic materials should be positive. Some resources like eFunda ...
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33 views

Thermal Conduction with multilayered system

Sorry this question probably has a really simple answer but I have been looking and I can't figure out how to solve this problem. I know that the equation for power loss through conduction is ...
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30 views

Heat Transfer in Cylindrical Coordinates

Lets say one has an infinitely long cylinder with some boundary heat terms on $r=r_0$ of the form $T(r=r_0, \phi,z)=T_0(\phi,z)$. What is the general solution for this type of equation? The general ...
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37 views

In supersonic flow, why must area increase in order to have velocity increase?

Based on the area velocity relation: $\frac{dA}{A}=(M^2-1)\frac{du}{u}$ For M > 1, in order to increase u, we must increase A. I'm wondering what the explanation is physically and why it is opposite ...
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216 views

Heat Transfer, Water in a pot

I have a question I've been pondering for a while. How can I determine the temperature in a pot filled with water? I know these things: I have a known mass of water, of mass $m_w$ I have a pot of ...
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74 views

Evaluate functional integral in partition function of thermal $\phi^4$ theory (Kapusta/Gale p.34-35)

my question is about some steps in the book "Finite Temperature Field Theory" by Kapusta and Gale. To explain the setting, I how to evaluate the functional integrals in the expression $$ \ln ...
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48 views

Electrochemical cell potential - Prigogine book

I'm trying to understand equation 10.2.14 from Prigogine book "Moder thermodynamics": $V=\frac{\tilde{A}}{nF}=\frac{1}{nF}\left(\mu_X^R+\mu_Y^L-\mu_{Xred}^R-\mu_{Yox}^L\right) - \left( \phi^R-\phi^L ...
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253 views

Ergodic Hypothesis; canonical ensemble

I'm currently studying for an exam in thermodynamics/classic statistical mechanics and 2 things came up which are confusing me. First the ergodic hypothesis states that it is equal to take the mean ...
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98 views

Could water physically makeup the core of a planet or otherwise large celestial mass?

Knowing very little about the nature of water, wondering how it might behave at the centre of a planet or centre of an another massive gravitational body. Could water take such pressures or might it ...
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85 views

Could CP violation be exploited to violate the second law?

I don't understand well CP-violation, but since it introduces a microscopic irreversible process, couldn't it be somehow exploited to decrease entropy? For instance, if we could somehow use it to bias ...
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497 views

VdW Gas Entropy/Enthalpy/Gibbs Free Energy of Mixing in 2 Chamber Experiment

What are the equations for $\Delta S_{mix}$, $\Delta G_{mix}$, and $\Delta H_{mix}$ for a real gas? Explanation: In one of the most well known experiments in thermodynamics, two chambers are ...
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103 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
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59 views

What's the connection between being homogeneous in energy and having a proper time scale?

Towards the end of page 8 of this scientific paper, I have found the following sentence: ...given the fact that the system is homogeneous in energy, or equivalently, that it has no proper time ...
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79 views

Medical/Physics Question - Cut Off Finger Preservation

This question might require some knowledge of medical/tissue, but physicists seem to know everything, so figured I've give it a shot here ;) When people put cut off fingers they are told to put the ...
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421 views

Finding internal energy using equation of state

I have an equation of state as a function of $p$ (pressure), $T$ (temperature) and $V$ (volume) for a real gas and need to find an expression for the internal energy $U$. I know this is given by the ...
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2k views

Basic Thermodynamics: Quasistatic Adiabatic Process

I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on: Show that for a quasistatic adiabatic process in a perfect gas, with ...
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89 views

What mechanisms require the use of different polarities in DC welding?

In gas metal arc welding, an electric arc forms between the work piece and a consumable wire, heating the work piece and also melting the tip of this consumable wire, which is continually fed into the ...
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194 views

Trace of the number operator in second quantization

I would like to find the helmholtz free energy of a system $F=-T ln(Tr[e^{\frac{-H}{T}}])$ namely a bcs superconductor (using Annett's notation) $H=\sum E_k (b_{k\uparrow}^\dagger ...
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59 views

Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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82 views

commutator to entropy in an uncertainty relationship?

Question: Does there exist a commutator to entropy in an uncertainty relationship? Similar Energy and time for instance.
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174 views

Heat equation with Neumann boundary conditions

I would like to explore some ideas with different geometries exchanging energy mainly by radiation. This means solving Laplace equation for the steady state. However the boundary conditions are always ...
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74 views

Is there a source that provides data for the temperature coefficient of resistivity at different temperatures?

I'm looking for a source where I can find the temperature coefficient of resistivity at different temperatures for pure metals. Tables are everywhere for 20$\,^{\circ}$C, but I'm having difficulties ...
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57 views

What's the domain of usability of these two expressions for entropy

$$dS=\frac{dQ}{T}$$ $$S=k\ln \Omega$$ What assumptions are being made about the system/process that allow for using those expressions?
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98 views

Can one get clear ice crystals from a dirty suspension?

Euteictic freeze crystallization is a method where an electrolytic solution is cooled and separated into a stream of (relativly) clean, pure ice and a salty brine. I know anectdotally of wine ...
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149 views

Calculate how hot PLA will become

I am trying to attach the shaft of a brass heating tip to a PLA component. My problem is that the tip will have to reach a temperature of about 200°C and the PLA can only handle a temperature of about ...
2
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71 views

Interface condition for heat exchange

I would like to compute the heat distribution of a piece of metal with some surrounding material. The heat is assumed to propagate by diffusion, so inside the metal piece and also on the outside, the ...