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Would a black teapot midway between the temperatures of the tea and air cool down or heat up? If neither, then how do the 3 reach thermal equilibrium?

An important part of learning about heat transfer is understanding the concept of steady-state flux or dynamic equilibrium. Here, a material may be furiously transferring heat while remaining at a ...
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1 vote

Would a black teapot midway between the temperatures of the tea and air cool down or heat up? If neither, then how do the 3 reach thermal equilibrium?

Let’s first suppose that we have a very large teapot with a relatively small surface area, so that the tea stays at the same temperature for a long time (this is called a “heat reservoir”). Heat ...
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How to derive Shannon Entropy from Clausius Theorem?

Yes, you can. Talk is cheap. I'll show you the formula. I'm going to show that the expression of the Shannon entropy can de deduced from statistical and thermodynamical relations. We know that the ...
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-1 votes

How does a steam turbine work in a closed loop?

i had been wondering something along the same lines and although the answer above makes sense, it may not be the most rational design. i am of the opinion that using one way pressure valves would be ...
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What does Specific Heat capacity of a material depend upon?

This is a complicated business which I will simplify a bit. Heating an object causes its constituent atoms to randomly vibrate more vigorously. In so doing, the atoms are continuously exchanging ...
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1 vote

Fake Perpetual Motion Device using an Electromagnet

Another way that this might work is that an electromagnet is turned on when the ball passes through the hole in the platform. This electromagnet would accelerate the ball faster than gravity towards ...
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1 vote

Metropolis-Hastings and underlying Markov process

I will answer as I found the mistake, my apologies for having been careless in posting I can assure you I spent much time doing hand calculations but sometimes things just evade your attention. The ...
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Metropolis-Hastings and underlying Markov process

Jumps between energy levels are not equally probabilistic, your transition matrix is just too arbitrary. First according to your definition $g_{ij}$ means that the particle was previously at energy ...
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1 vote
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How to calculate integrals in Ideal Fermi Gas theory?

As mentioned in the other answer, we can take $\mathbf{q}$ to point in the $z$-direction: $$\int \frac{d^3k}{(2\pi)^3} \theta(k_F - k)(\mathbf{k}\cdot\mathbf{q})^n = \int d\Omega\int_{0}^{k_F}\frac{...
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1 vote

Non-Work energy conversion

Work is a more general concept than a force acting through a distance. The mechanics branch of physics primarily addresses work for a point particle, or a rigid body, for which there is no change in ...
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Non-Work energy conversion

In thermodynamics, work is a macroscopic notion, as a piston being moved againt some load. We could think of a kind of work-energy stuff when heat increases the kinetic energy of a gas (by increasing ...
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-1 votes

How to calculate integrals in Ideal Fermi Gas theory?

The integral is spherically symmetric so we can put $\mathbf{q}$ along the $z$-axis: $$\int \frac{d^3k}{(2\pi)^3} \theta(k_F - k)(\mathbf{k}\cdot\mathbf{q})^n = \int d\Omega\int_{0}^{k_F}\frac{k^2dk}{...
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2 votes

Does passing an electric current along a strip of metal submerged in saltwater cause anything?

Yes. Pumping current into the hull of a ship in moored storage has been used for decades to prevent the hull from corroding in constant contact with sea water. To accomplish this, a very large carbon ...
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Intuitive understanding of the derivation of the Rayleigh-Jeans law

I guess I am struggling with the 2nd argument which was there is no limit on the number of modes of vibrations that can excited? Why would there be no limit? Can someone please explain? This follows ...
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How do you calculate the fugacity for a Van der Waals gas at low pressure?

$$RTd\ln{f}=vdp$$where v is the molar volume. So, $$RTd\ln{(f/p)}=\left(v-\frac{RT}{p}\right)dp$$ subject to the condition that (f/p)=1 at p=0
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Why is Gibbs free energy not used in Statistical Associating Fluid Theory (SAFT) Equation of State (EoS)?

Statistical Associating Fluid Theory (SAFT) Equation of State is a popular approximate method, based on perturbation theories of Statistical Mechanics, able to incorporate the effects of molecular ...
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1 vote

Can radiant heat (as felt near lava) be measured as a temperature?

Sure, but there are lots of "caveats" going with the subject. The first place to look is the subject of pyrometer. Here is the wiki article, but be sure to google the subject and pick out ...
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How comes, that my book states that internal energy is dependent on volume?

The specific internal energy of an ideal gas is a function of temperature only. Using standard engineering thermodynamics nomenclature a system (open or closed) has a certain mass (that can vary with ...
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1 vote

Boltzmann vs Gibbs definition of entropy

Provided that the average of a quantity is defined by $$ \langle A\rangle = \sum_i P_i A_i, $$ the entropy by definition can be viewed as the average of the negative logarithm of the probability of a ...
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1 vote

Small parameter expansion to obtain convective heat transfer solution of the heat equation

First, let me note that the dimensionless equation in the OP has an incorrect factor, it should read: $$ \frac{\partial}{\partial \theta}u=\frac{1}{2}\frac{\partial^2}{\partial \xi^2}u+\varepsilon_V\...
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3 votes

To clarify the entropy/ energy/ Gibbs Eqs

Initial State: $$T_1=313\ K$$$$V_1=V$$$$n_1=n$$$$P_1=\frac{n_1RT_1}{V_1}=\frac{nR(313)}{V}$$ Final State:$$T_2=313\ K$$$$V_2=V$$$$n_2=n$$$$P_2=\frac{n_2RT_2}{V_2}=\frac{nR(313)}{V}$$ The final state ...
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Entropy change of the ideal gas

I wonder if there is something wrong with δQ=δW There is nothing wrong. From the first law $$\Delta U=Q-W$$ For an ideal gas, no matter what the process, any change in internal energy $\Delta U$ ...
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2 votes

Source of light in a heating coil

The interactions/collisions between the free/mobile electrons and the lattice ions/atoms/molecules cause them to vibrate. Ions/atoms/molecules are complicated arrangements of electric charge. When an (...
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1 vote

Why Gibbs free enthalpy is not zero?

This formula isn't universally valid. Free enthalpy's definition is $G=E+PV-TS$, so, for a system without chemical reaction or phase transition: $$dG=dE+PdV+VdP-TdS-SdT=VdP-SdT$$ So if $P$ and $T$ are ...
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Do Maxwell's equations still apply in fluids?

The "macroscopic formulation" of Maxwell's equations (linked by others in the comments) are often called "Maxwell's equations in matter" because they account for the fact that ...
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-3 votes

The ideal gas equation is $pV=nRT$. Prove that $p=\frac{\rho RT}{M}$

Mass ($M$) = Density ($\rho$) x Volume ($V$) $$V=M/\rho$$ Put it in $PV=nRT$ ----> $PM/\rho = nRT$ This gives us $\rho = PM/nRT$. So $M/n$ can be converted by mole concept but it totally depends on ...
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7 votes
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The ideal gas equation is $pV=nRT$. Prove that $p=\frac{\rho RT}{M}$

Would the mass of ten apples change if you moved the apples to another location? The principle is essentially the same here - a mole of a gas is just a particular number of gas atoms.
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-1 votes

Why does Triple point exist?

Because liquids don't exist∗. A liquid is just a wannabe gas. There are two phases of matter - solid (cold) which turns into gas (hot) at a certain temperature (273 K for H₂O). This process is called ...
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1 vote

How to derive Shannon Entropy from Clausius Theorem?

A better approach would be to use the Shannon Entropy to derive Gibbs entropy: $S=−k\cdot∑p_n \cdot \ln(p_n)$. The two equations are very similar and therefore it is much easier understand. From ...
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3 votes
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How to derive Shannon Entropy from Clausius Theorem?

You can't. It is not possible to derive a more general formula from a less general one. Of course, one can find hints for the generalization, but the validity of the generalization has to be proved ...
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4 votes

How to derive Shannon Entropy from Clausius Theorem?

These are not the same. Shannon entropy (Information entropy), $H_\alpha=-\sum_i p_i\log_\alpha p_i$ applies to any system with specified probabilities $p_i$. Boltzmann entropy, defined via the famous ...
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Understanding the derivation of the variational principle in classical density functional theory

eq(4) and eq(5) are equivalent. First I rewrite eq(5) as the result of $f_N = \rho^{(N)}$ in eq(1): $$\Omega [\rho^{(N)}] = \mathrm{Tr_{cl}} \left[ \rho^{(N)} \left( H - \mu N + \beta^{-1}\ln{\rho^{(N)...
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Is it easier to gain energy or to lose it?

I don't know. The way I see the problem, the two containers of water conform the water to identical-shaped cylinders with the same surface area. In both, 40°C of energy must pass through this surface ...
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Changes to a thermometer that would require the spacing of the division to be larger

The stress here is on the meaning to the word "accurate". Suppose that a given liquid thermometer has accurate tick marks at 1, 2, 3, ... This means, when the level is EXACTLY at that tick ...
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How do you calculate the "true" chemical potential in classical density functional theory?

This isn't a detailed answer; hopefully I can come back and answer it more fully later. However, here is a simple explanation that might help. Instead of taking the functional derivative of the ...
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1 vote

How do you make light?

How about an AC electric circuit attached to an antenna - like any radio, cellular, or TV transmission tower. Granted it takes a bit of work :-) to make an oscillator in the visible-spectrum ...
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1 vote

Would water flow in the following system?

Short answer: it depends! Longer answer: If the temperature of the water in the tank is uniform and the peltier is able to reduce the temperature of the water, ther will be a flow of water. At least ...
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1 vote
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How do you make light?

Quanta of em radiation called photons are produced in many reactions involving fundamental particles, atomic nuclei or whole atoms. These include thermal vibration of atoms and molecules; transition ...
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0 votes

What properties of a mixture can be calculated?

Wikipedia article on Dalton's law lists several other "laws" for various quantities in gas mixtures: some of them simply add (like pressures in the Dalton's law), while the others add with ...
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0 votes

$\rm CO_2$ Car Back Wheel Thickness

You are correct that the increase in rear wheel width will not enhance the linear rolling performance of your vehicle since the vehicle is using thrust. It will add to the drag of your vehicle. I've ...
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0 votes
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Does gas pressure impact the rate of evaporation?

Does pressure of the gas above the liquid have any impact on the number of liquid molecules escaping into the vapor phase? Yes. If the pressure is low enough, the net rate at which molecules in the ...
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0 votes

$\rm CO_2$ Car Back Wheel Thickness

I don't see what the advantage is of thicker back wheels. Rolling resistance force is defined as : $$ F_{rr} = \sqrt {\frac zd}~N $$ where $z$ is sinkage depth and $d$ - wheel diameter. Sinkage depth ...
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In the Statistical Mechanics Mark E. Tuckerman 4.4.7

The author indicates that $C_V$ is an extensive quantity, that is, it is proportional to the amount or quantity of material. The latter quantity is indeed $N$, the number of particles in the system. ...
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-2 votes

Why do most metals have high thermal expansion coefficient although their thermal conductivity are generaly high?

Most metals have high electron shells....this propensity to give off electrons. The reactivity of elements are related to the number of electrons in their outermost shells. Where as the Atoms of metal ...
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1 vote

Is it possible for a thermoelectric generator to not have a heat source or heat sink?

No. From the thermodynamics point of view, performing useful works requires heat transfer from a warmer body to a colder one, and there is no way of converting all the heat into useful work. This is a ...
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Quantum versus Classical Partition Function

For a classical system defined on a phase-space $\{q_1,...,q_n,p_1,....,p_n\}$ and a Hamiltonian $H(\{q_n,p_n\})$ the partition function for a canonical ensemble is given by $$Z_{\text{classical}}= \...
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3 votes

Why do most metals have high thermal expansion coefficient although their thermal conductivity are generaly high?

The high thermal conductivity and high thermal expansion of metals have somewhat different origins, although they both can be traced back to the metallic bonding and band formation. For thermal ...
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2 votes
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Clearing up concepts regarding quasi-static processes

This is an annoying problem, I agree. I find that the most useful definition of a quasi-static process is: a process during which the system reaches internal equilibrium at every instant. Internal ...
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2 votes
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Quantum versus Classical Partition Function

Formula $(1)$ can be considered a general, formal expression valid for classical and quantum systems. The critical point is to have clear in mind the meaning of the summation index $i$. The partition ...
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1 vote
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An ideal gas expands into vacuum in an insulated rigid vessel. Which of the followings happens?

I think this could be their point of view, consider a rigid vessel with two chambers seperated by a partition. In this vessel, one of the chambers is filled with the ideal gas and the other chamber is ...
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