Tagged Questions

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Entropy of a two-level system

Consider a two-level system with energies and degeneracies $\epsilon_0 = 0, g_0=1$ and $\epsilon_1 = \epsilon, g_1=4$. I can show that the temperature at which both levels are equally populated is ...
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Chandrasekhar Limit [closed]

A white dwarf is essentially a degenerate electron gas, in which pressure of degenerate electrons supports gravitational pressure. As a simplified model of such an object, consider a spherical star of ...
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state on quantum statistics. 3 particles according to 3 distributions [closed]

consider a system of three identical particles, A B ,and C. Assume that each particle can be in one of three possible quantum states, 1,2 and 3. For the following statistics listed below, enumerate ...
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Calculation of the differential of the entropy

In this review (for those who wants a precise reference see page 8 eq 21), the Author says that: \begin{equation*} S=-\sum_{i}P\left(i\right)\ln P\left(i\right) \end{equation*} and using the ...
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Coarse-graining on a second channel decreases mutual information?

Let $X_1,B_1,X_2,B_2$ and $Y_1,A_1,Y_2,A_2$ and $C_1$ and $C_2$ be binary random variables. Suppose: $I(X_2:B_2|C_2=0)+I(Y_2:A_2|C_2=1) \leq 1$. This can be thought of as a bound on the capacity ...
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Temperature limit on entropy of a paramagnet

We have $$S=Nk_B[\ln(2 \cosh(x)) - x \tanh(x)]$$ where $$x = \frac{\mu B}{k_BT}$$ In need to show that at low temperatures entropy $$S \approx Nk_B2xe^{-2x}$$ I wrote out the $\cosh(x)$ in terms of ...
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Canonical partition sum for two fermions in harmonic potential

In an old exam, I found the following problem: Two Particles in a potential well We look at a onedimensional harmonic potential well that hold two spinless particles that do not interact with ...
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Equation of state of a rubber band

I have the following question that I attached in png format. I have done part (a), but I am having difficulties in part (b) when I proceed according to the book. I have non zero tension at ...
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Must a reversible engine be a carnot engine?

I have this homework question: "Show that any reversible engine operating between T1 and T2 is a carnot engine." I think I have a solution, but it feels very hand-wavy. We know that any process that ...
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Entropy of a particle with two energy states [closed]

A particle has two energy states having energies $E_0$ and $E_1$ with degeneracies $g_0$ and $g_1$. The respective probabilities are $p_1$ and $p_2$. What is the entropy in terms of $p_1$, ...
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Ensemble of harmonic oscillators

I have some problems with problem 2.3 from Reif's Fundamentals of statistical and thermal physics: Consider an ensemble of classical one-dimensional harmonic oscillators. a) If we assume ...
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Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through ...
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Magnetic Susceptibility at Arbitrary Temperature

I'm currently working on an assignment where the questions is: Consider a gas of N noninteracting electrons in a uniform magnetic field B = B$\hat{z}$ in a macroscopic system. Assume that the ...
In Wikipedia's article on Fermi Gases, they have the following equation for the chemical potential: $$\mu = E_0 + E_F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{E_F}\right) ^2 - \frac{\pi^4}{80} ... 0answers 446 views Density of states of a photon gas in volume V and temperature T I have a question on the density of states for a photon gas: Suppose I have a photon gas in a box of volume V at temperature T. If I enumerate the total number of states accessible to the system ... 2answers 458 views 1 dimensional Ising model How to solve the Ising model in 1D by low temperature, and high temperature expansion, and by change of variable method? Can you please give me some reference links? 1answer 166 views Bose–Einstein statistics exercise I've a basic Bose–Einstein statistics exercise. I've tried to solve it in two ways, but each way gives a different result. We have n identical bosons without interactions at temperature T. There ... 0answers 60 views error propagation and collision in ideal gas When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ... 0answers 154 views Maxwell-Boltzmann distribution The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function. What I currently need to solve is: {{\mathcal{L}}^{\,\left( ... 0answers 129 views Maxwell-Boltzmann distribution for transport equations I have to calculate the transport coefficients for the Maxwell-Boltzmann distribution. But I'm not sure what distribution I have to use. As far as I know it should not be the MB distribution for ... 2answers 224 views Calculating the change in entropy in a melting process I have a homework question that I'm completely stumped on and need help solving it. I have a 50\, \mathrm{g} ice cube at -15\, \mathrm{C} that is in a container of 200\, \mathrm{g} of water at ... 1answer 204 views Energy density of a quantum mechanical ensemble How do we determine the energy density of a given system? I have seen that the density operator$$\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$What does this mean exactly ... 1answer 180 views Basic energy calculation for N identical spin system We have a system that has N identical spins n_i, and each spin can be in state 1 or 0. The overall energy for the system is \epsilon\sum_{i=1}^{N}n_i. My understanding: There is only one ... 1answer 40 views How can I find the temperature of this system? A system was given a small amount of thermal energy dE, and its number of states G grew by 25%. How can I find the system temperature? The system contains gas particles, I know that dE << ... 1answer 139 views Maximizing Multiplicity of Einstein Solid == (Temperature = \infty)? If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ... 2answers 315 views Energy of particle in electric field I'm taking a physics class and the professor teaches us really basic things in lecture and then gives homework way beyond what he taught in lecture. Obviously I need to find some resource other than ... 0answers 414 views Pauli paramagnetism for electrons with external magnetic field Apparently it is to be shown that for electrons under an external magnetic field, in the limit as B\to 0$$ \chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)} $$... 0answers 291 views Rotational Constant and Moment of Inertia of Fluorine gas I have come across some homework question on thermodynamics which needs me to calculate B of F_2 My attempt: B= \frac{h}{8\pi^2cI} where I=\mu r^2=\frac{m_1m_2}{m_1+m_2} r^2 Atomic mass of ... 2answers 475 views Canonical partition of a boson gas I have a 1D gas made of N particles placed in a harmonic potential well, so the Hamiltonian is:$$ \mathcal H = \sum_{j=1}^N \left ( \frac{p_j^2}{2m} + \frac{1}{2}m\omega^2 x_j^2 \right ) The ...
Let us consider a square grid, which has been rotated by 45deg. On this grid we deﬁne a path, the directed polymer, which starts at the origin ($t = 0$) and extends in the positive $t$-direction ...