# Tagged Questions

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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### Does relativity objectively define entropy?

In his undergraduate text "Spacetime Physics", Wheeler points out that there is always a fourth component to momentum and energy interactions, because the internal motion of the objects involved will ...
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### Calculation of entropy change in irreversible cycles, meaning of $\delta Q/T$ in irreversible processes

Let's take the two cycles in the pictures working with an ideal gas. We perform one, and then perform the other. The cycle is made reversible by making the gas exchange heat with a heat bath having ...
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### The outside of a steel teapot is hot to touch. Does this mean that the water inside is necessarily at least as hot?

Some teapots, like this one Are made from thin steel which conducts the heat of the teapot quite well, meaning that you can't comfortable hold the sides while they're full of hot water. Tonight I ...
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### Finding the expression for the time it takes for a water tank to be half empty

The problem is to find an expression for the time it takes for a cylindrical water tank is half empty. I am given that the water tank has a diameter of $D_0$ and a hight $H$. The water outlet is ...
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### what is the temperature (and pressure) of the oxygen inside an oxygen bottle?

In the hospital or in a lab, one can see the huge oxygen bottles. A question is, what is the temperature of the oxygen inside the bottle? And what is the pressure inside? We know the critical ...
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### Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the ...
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### Why should slope of pressure versus volume always be negative?

I read that the slope of the pressure, ($P$), versus volume ($V$) graph should always be negative for thermodynamic stability, but there was no further explanation in the text. Could someone give an ...
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### Feasible way to cool water (ice) to temperatures around -20 degree celsius

Is there an easy way to cool water to temperatures around -20 or -30 degree celsius that is economically and technologically feasible for a high school student. Can it be done using typical household ...
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### 2nd law of thermodynamics - thought experiment

I have designed this simple thought experiment that seems to contradict 2nd law of thermodynamics. Could you please find a mistake in my reasoning? ...
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### Planck's postulate for oscillators or for light?

I know that Planck originally postulated that the energy of an oscillator in a black body was quantised to $E=nh\nu$ but did he know at the time that this meant the energy of light was also quantised (...
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### Sufficient conditions for Equipartition Theorem to hold

I was wondering what are the sufficient conditions for the Equipartition Theorem. I know there is another question (For which systems is the equipartition theorem valid?) that somewhats answers this ...
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### Any general method of determining changes in speed of sound with pressure?

I need to correct speed of sound measurements in various gases for changes in ambient pressure, typically 700-1100 mBar. Is there any general theoretical model available for this? Especially something ...
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### Steady State For An Air Conditioner

Here's the problem I'm trying to solve (from Blundell's Concepts In Thermal Physics): I just don't understand what "steady state" exactly means here. Does it mean that the temperature of the house ...
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### What is a “fundamental thermodynamic relation”?

My professor handed me a quiz in which he said something like (I don't remember exactly) "write down the four fundamental thermodynamic relations for $A,G,H,U$". I showed the differential elements of ...
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### Is Carnot engine the only reversible engine?

Is Carnot engine the only form of reversible engine? Is it possible to have a different form of reversible engine that goes through different processes? For a standard Otto cycle working with ideal ...
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### How are specific volumes accurately measured experimentally?

In every thermodynamics textbook there are tables containing the specific volume of various fluids at different temperatures and pressures. My question is, how is this data obtained experimentally? ...
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### Is heat a property of Something?

There are some unique properties of things in our world. For example, charge is a property of mass. Is heat a unique property of something? Can a vacuum/void have a finite amount of heat in it? What ...
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### Energy Flux due to Diffusion

Per the Fundamental Thermodynamic Relation, I know that the chemical potential of $i$ represents the energy which would added to a system if a particle of $i$ were added with all other system ...
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### Does the conductivity of a wire in a vacuum decrease over time?

Does the conductivity of a wire in a vacuum decrease over time, say over the period of years or decades? In other words: Does current degrade a wire, making it less conductive? If so, by how much, and ...
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### Why does the Nusselt Number for a Constant Surface Temperature, Thermally Fully Developed Circular Pipe Converge To a Constant of 3.66?

I have flow in a pipe with a constant surface temperature boundary condition. The velocity profile is fully developed and the temperature profile is also fully developed. In my textbook, it says that ...
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### Why do windows fog quickly?

I'm from Bogotá, Colombia. In my city the temperature is all the year between 12ºC and 25ºC (bus mostly under 19ºC) and when I drive and it's raining, there is accumulation of fog on the windows, but ...
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### Why does a substance expands upon freezing? What conditions necessitate this?

Why does a substance expands upon freezing? What conditions necessitate this? For example, how does the slope of sublimation or fusion curve in a P-T diagram affect this?
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### Derivation of the Maxwell-Boltzmann speed distribution

We're currently deriving the Maxwell-Boltzmann speed distribution, but I'm struggling to squeeze out the right answer. For the first exercise we have to derive the fraction of molecules travelling ...
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### How stable are Benard Cells when the thermal gradient begins decreasing?

I've found lots of information on the formation of Benard Cells and convection currents but very little information about what happens to the self-organized structures when the energy gradient being ...
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### Expectation value of $a_i^\dagger a_i$ for thermal density matrix

Suppose we have some heat bath with Hamiltonian, $$H=\sum_n \left(a^{\dagger}_na_n+\frac{1}{2}\right)\hbar\omega_n$$ and a density matrix $\rho=Z\exp(-\beta H)$ for some normalisation $Z$. ...
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### Simple modelling of seasonal variation of temperature?

I'm really curious about this: What is the simplest (or most simplified) differential equation that accounts for the variations of temperature throughout the year at some point on the northern ...
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I quickly plunged a room-temperature thermometer into very hot water, the mercury level went down briefly before going up to a final reading. Why?
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### A gas close to zero Kelvin

Consider an adiabatic expansion of an ideal gas that work is done against friction or a piston. Since no heat exchange can occur the gas keep on losing energy and its temperature decreases and the gas ...
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### How much electricity could be generated by cloths made of thermocouples?

Lets say that we made a glove, shirt, pants and a hat out of the most effective thermocouple material available today. How much electricity would be generated by each, by a healthy person, on a cool ...
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### Why does my house seem to warm faster in summer than it cools in winter? [closed]

In summers when we switch off the air conditioner, the room seems to instantly get hot again. But in winter, when we switch off the heater the room seems to remain hot for some time. Why this ...
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### role of entropy in gibbs free energy intuition

I have looked at various derivations of the Gibbs free energy equation and the underlying definition of the gibbs free energy. However I have been unable to attain direct insight/intuition over the ...
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### Can 'Backradiation' warm its own source? [duplicate]

Ok, although this question arises out of the global warming debate, this is a question purely for physicists and not intended to branch into that particular debate. We are told that LWIR from the ...
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### System in mechanical but not thermal equilibrium

Let's say there are two systems which can interact by a moving wall but cannot exchange heat. Then the system will be in mechanical, but not necessarily in thermal equilibrium. The maximality of ...
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### Container divided in two parts with ideal gas

I wanted to ask your help with the following problem: Consider a closed container, that is, with insulated walls impervious, and rigid. The container is divided into two parts by a wall having the ...
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### How to calculate fluid's temperature change in a pump?

To calculate the pressure at the outlet of a pump we use pump performance characteristics i.e. charts giving pump head as a function of volumetric flow. When the fluid flows through a pump, it's ...
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### Details in the derivation of the second law starting from the phase space volume

I had a question on one of the details of the derivation of the second law of thermodynamics starting from the phase space volume. I'll type out what I understand so far: Letting the Hamiltonian ...
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### How do I calculate the curve of a parabolic mirror to melt the ice from my street gutter?

I want to make a concave parabolic mirror that will have a focal point six inches below where I place it (on the edge of the sidewalk) so that it will melt the ice collecting in the gutter below and ...
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### Change of heat capacity fluid when you add solvent

I am considering a liquid for which I know $C_p$ or $C_v$. I am wondering how this changes when you add a (minor) amount of solvent to the liquid. Is there a general theory around describing how a ...
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### Probability of Different States - Canonical Ensemble - Partition Function

Consider a canonical ensemble of $N$ ideal gas atoms, which could have spin up or spin down. Why is it that the probability of finding the particle in a spin up state generally only involves the ...
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### How does that Boltzmann distribution interact with entropy?

In an ideal gas, the Boltzmann distribution predicts a distribution of particle energies $E_i$ proportional to $ge^{-E_i/k_bT}$. But, doesn't entropy dictate that the system will always progress ...
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### Volume quotient in Carnot-cycle

Problem: One kilomole of an ideal, monatomic gas undergoes a reversible Carnot-processes between temperatures 300 °C and 20 °C. The work done during one cycle is 1500 kJ. a) Find the entropy-...
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### Why is $0 \,\mathrm{K}$ so special?

I know that $0 \,\mathrm{K}$ cannot be reached, this is discussed here and here. But, why is it such an important statement? I mean, there are many properties which will never be zero, like: ...
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### Does serving food on a hot plate really keep it warm longer?

I live in Ireland where serving food on hot plates is considered “good cooking practice” to ensure the food remains warm – I come from France where I have rarely seen it done. I am wondering if this ...
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### Deriving the condtion for spontaneity using gibbs free energy

While deriving the condition for spontaneity, $\Delta$G$\leqslant$0, we start by saying that $\Delta S_{tot}$ $\ge$0 $\Rightarrow$ $\Delta S_{sys}$ + $\Delta S_{surr}$ $\ge0$ If $Q$ is the heat ...
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### Pressure derivatives of the bulk modulus of materials? (Solved) [closed]

Isotherm bulk modulus is defined by $$K=\rho\left(\frac{\partial p}{\partial\rho}\right)_T=-v\left(\frac{\partial p}{\partial v}\right)_T$$ wherein $v=\tfrac{1}{\rho}$ is the specific volume. Studying ...
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### Clarification on the Seebeck Effect

Alright, I've been interested in the Seebeck effect lately, so I've been trying to learn it. From what I understand, this is measured with the Seebeck Coefficient, which gives you the $\mu\textrm{V}$ (...
Assume the following phase diagram $T-H$ of water At a nuclear engineering course, I was told that in order to increase the performance of a pressurized water reactor, one has to increase the ...