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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2 votes

Thermodynamic entropy vs statistical mechanical entropy

Because entropy is a function of state, this computation can be assumed to be performed in an equilibrium state, where it holds that $T_{b} = T$. It just makes more sense to talk about the system's ...
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2 votes

How could we estimate the number of molecules below which a fluid cannot be adequately modeled by the Navier-Stokes equations?

Whether the Navier-Stokes are or not a valid model is dictated by the Knudsen number: $$Kn=\frac{\lambda}{L}$$ Where $\Lambda$ is the mean free path of the fluid and $L$ is a characteristic length ...
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2 votes
Accepted

Will the calculated mathematical probability of a decrease of disorder in mixing of gases violate the second law of thermodynamics?

Your understanding of the concept of entropy is wrong. Entropy is a statistical property that does not depend on a specific microstate, but rather a group of theoretically allowed microstates. As you ...
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2 votes
Accepted

Why does temperature remain constant in this case?

It is a consequence of the first law of thermodynamics applied to the whole system. Since the whole system is isolated $dU=dU_1+dU_2=0$, also at equilibrium the final temperature of the two ...
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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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1 vote
Accepted

Rankine Cycle $pV$ diagram

but process 3-4 that's isentropic compression in the pump is in fact shown as isochoric. There's no contradiction here. A process can be both isochoric and isentropic. In this case it's considered ...
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1 vote

Work done by an ideal gas in an adiabatic free expansion

This gets solved by noticing that Work is not an state function. While you can calculate the entropy by choosing another connecting process between the final and initial states you CAN'T do that for ...
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1 vote

What will happen if the inner walls of the perfect blackbody (shown in the image) is made perfectly reflecting?

Q1: If light can come in through the opening, it can also come out through it. So it isn't possible to concentrate energy inside arbitrarily. Reflecting walls means the outgoing radiation spectrum ...
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1 vote

Using quasistatic processes to calculate quantities

The answer to your first question is, as you suspected, that there is no adiabatic reversible path between the same initial and final states for an adiabatic irreversible process. We know this ...
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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?

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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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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1 vote
Accepted

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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  • 7,275
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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  • 6,228
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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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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  • 37.4k
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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