# 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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### Thermodynamics Heat flow into Ideal Gas

I'm currently looking at University Physics by Young and Freedman, and I came across a problem that is stumping me. 19.25. Heat $Q$ flows into a monatomic ideal gas, and the volume increases while ...
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### Mono-atomic gas particles coupled by spring forces don't care how many particles are involved?

I calculated the partition function of $N$ classical atoms of identical mass $m$ who all experience a mutual spring forces with identical spring constant $k$. The Hamilton is \begin{align} H = \dfrac{...
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### Does the density of water ice (any form of water ice) near 0K exceed the density of water at 277.15K?

In a question brought up by my chemistry class, the most we have determined is that the stability of most forms of ice decreases as the temperature decreases. What does this loss of stability do to ...
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### Can the energy/power required to mix two fluids together be calculated?

Given two fluids; say for example oxygen and nitrogen gases. By simply introducing, again for example 1 liter of each gas into a closed container, the process of diffusion alone will eventually cause ...
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### 7/2 versus 9/2 for diatomic heat capacity

Question I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$. I assumed the classical Hamiltonian of two identical atoms ...
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### Dependence of heat absorbed on different ways of heating

Heat capacity depends on the delta Q (i.e small amount of heat absorbed) and delta T (i.e small change in temperature). My question is,why is the amount of heat absorbed different for different ways ...
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### Thermodynamic transformation

Why is it that any reversible thermodynamic transformation is quasi-static? Also, why is the converse not necessarily true?
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### Nature of system taken in thermodynamics

Why is thermodynamic system always taken as macroscopic ? What will be the changes if one considers the same as microscopic ?
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### Is it true as entropy increases things become more symmetric?

Is it true that as entropy increases in a particular domain (say, the universe or a given box) so do the symmetries within this domain? Are there exceptions? Say I'm looking at a rotational symmetry. ...
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### What is the entropy of a mixed state in classical physics?

Consider a classical system which admits certain macroscopic level of description. It is known, that for two pure states $\omega_1$ and $\omega_2$ on this level of description the entropy of the ...
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### Internal energy in phase transition

As I understand, in the process of state transition (fusion or vaporization) the temperature remains constant for the duration the process is happening. The internal energy is a function of only ...
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### Is the energy per degree of freedom $\frac{1}{2}kT$ in relativistic systems?

The equipartition theorem says that the mean energy per degree of freedom is $\frac{1}{2} kT$. Is this result relativistically correct?
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### relation between speed and temperature in relativistic gas

What is the correct formulation of the relation between the speed and temperature in the relativistic kinetic gas? I have found one mentioned in problem 3.24 of the third edition of Pathria's ...
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### Is amount of entropy subjective?

From all sources I have seen it follows that the proof you can't decrease the amount of entropy in the Universe is given only statistically - the order is just one of the many ways how things can be (...
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### first law of thermodynamics and conservation of energy

The first law of thermodynamics is referred to as a reformulation of the law of conservation of energy. I am not sure to fully understand this relationship. My way of picturing it is the following. ...
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### Why can't the energy gained due to entropy be used for doing work?

Gibbs energy is defined as the energy 'available' to do work at constant temperature & pressure.The energy required to make the system from none under constant pressure is the enthalpy, that must ...
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### Really how does the entropy of the universe increase?

Universe means the system along with its surroundings. I have always got this statement while studying the second law; be it a thermodynamics book (Sears, Salinger) , physical chemistry book (Atkins, ...
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### Free energy of coupled classical harmonic oscillators

I'm looking to find the thermodynamic (NVT) free energy of a classical coupled harmonic oscillator system such as the one below: (image taken from http://openmetric.org/StatisticalPhysics/...
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### Does a venturi injector contradict the 2nd law of thermodynamics?

The picture below shows a venturi injector. When the water flow enters the narrower cross section its velocity increases and its pressure decreases. Subsequently, fluid is sucked (or injected) into ...
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### What are the distributions of electron speeds in a star and in a planet?

Ideally I would like to have an $x$-$y$ graph of ($x$) speed relative to centre of mass of the body (star or planet) against ($y$) the number or percentage of electrons having that speed at a given ...
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### How to calculate electrical and thermal conductivity, enthalpy and density of plasma column in air for a series electric arc?

I am modeling an electric arc according to "Lowke's Simple theory of free burning arc". Its a very interesting theoretical arc model and I want to implement it in Matlab/Simulink. But here, the arc ...
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### Uniqueness of solution of Laplace's equation

Consider steady-state temperature in a rectangular plate; we get solution when we solve Laplace's equation. In the midway of solving this equation, we take linear combination of basic solutions and ...
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### Thermodynamics - Possibility of Cold radiation

I am no physicist, let’s just get that out in the open, I'm just a guy with an interest in this area. One thing I have learned in my limited examination of the natural world is that things tend to ...
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This makes absolutely no sense to me. My physics book states the following (University Physics 12th ed, Pg 650) Suppose we want to change the volume of a certain quantity of an ideal gas from 2.0 ...
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### Gibbs phase rule and degrees of freedom at the triple point / triple line

The Gibbs phase rule tells me that at a substance's triple point, where there are 3 phases in equilibrium, there should be 0 degrees of freedom. Based on my understanding, that means there should be 0 ...
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### Calculate pressure with the ideal gas law or $\rho gh$?

In a container the pressure on the walls due to a gas can be calculated using the ideal gas law $\bigl(pV=NRT\bigr)$. However, for a column of water, or the pressure at earth's surface due to a ...
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### Was the impossibility of the second degree perpetuum mobile in the General Relativity ever proven?

Somewhere I've heard, that gravity often likes to work against the entropy. For example, the surprisingly low temperature of the black holes. Or see the gravitational separation of different elements ...
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### Can higher level animals have lower entropy than the food they consume?

If there is plant source of energy 100Cal and an animal source of energy 100Cal for a human being, where the animal derived that energy from a similar plant source, can we say for sure that the animal ...
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### energy efficiency - dryer vs hang+dehumidifer

When I have wet clothes coming out of the washing machine, I can either tumble-dry them in an electric clothes-dryer, or I can hang them to dry. But I can only hang them in a basement. The basement ...
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### Temperature of planets without atmosphere

I am wondering how come a planet without atmoshhere loses heat in space when the space around it is a vacuum. In my understanding for one object to lose heat it must have contact with another object/...
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### Does stopping the same bike and rider at the same velocity with the front brake require less energy than the back brake?

It's the same body made by the rider and the bike moving at the same speed. So, even though braking on the front/back alters the normal forces on the opposite wheels thus creating more friction with ...
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### Why do we ignore rotational energy in monatomic gases? [duplicate]

I understand that the average energy of each degree of freedom in a thermodynamic system is $\frac12kT$. And so, for an ideal monatomic gas, there are three degrees of freedom associated with the ...
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### Find an expression for S(T,x) from tension and specific heat

I'm working on a problem from a Statistical Mechanics lecture series online, and on the homework, I hit a bump in this problem. Here is the problem set, and I'm asking about #1.c. Short version, we ...
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### How do I calculate the change in water temperature as a function of depth?

Let's say I have ground water at a depth of $3000m$ at $50^{o}C$. If I now pump this water up to the surface, the water pressure decreases from the $\pm 300 atm$ at that depth to $1 atm$ at the ...
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### Finding the Enthalpy of an Ideal Gas given internal energy

I am trying to find a formula for tying things up. Given an ideal gas like helium or nitrogen gas (diatomic) how can I find its enthalpy simply given internal energy? I remember it was once taught in ...
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### Rapid/ Slow Expansion in Gases

How is rapid expansion of gases different from slow expansion?
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### Can I measure the volume of a locked room by pumping gas through keyhole and measuring its entropy?

Suppose that I have a locked room and a keyhole in the door and I want to measure the room's volume. Suppose also that I have some "magical" "artificial" inert gas A that doesn't interact with ...
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### How does the heat death looks like from inside the system?

As this answer points out, any human would first freeze rather than experience the heat death. However, assuming hypothetically that we could make some robot live at such low temperature (or even ...
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### Understanding the Carnot cycle

My textbook explains the Carnot cycle as follows: Heat is added to the boiler, where the steam inside expands isothermally at high temperature (T(High))--(both valves closed). The intake valve is ...
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### Water enclosed in a vessel

Suppose I am taking water in a glass or metal or even something else. It s air tight and (so it is water tight). Now imagine, if I keep it heating and none of its molecule escapes from it, what am I ...
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### Two glass bottles of water warming by different temperatures

A friend posed a question to me yesterday: if I have two glasses of 60 F water, would they heat at a different rate if one were in a 70 F room and one were in a 90 F room. Myself having some ...
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### Should the weaker of two air conditions be switched off?

We have two airconditioning systems in the office. For the sake of this question, let us assume the following current conditions: AC1 (old) outputs air of 26°C AC2 (new) outputs air of 18°C Office ...
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### Distinguishing Isentropic Process; Are all things in an insulated cylinder considered reversible adiabatic?

How much work is necessary to compress air in an insulated cylinder from 0.20m^3 to 0.01m^3. Use T1 = 20C and P1 = 100 kPa. I don't need to solution or the answer. I already have it. But I think ...
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### Help recognizing partial differential equation

I would be very grateful if someone could tell me something about the following partial differential equation:  \frac{\partial U}{\partial t} = K * (\frac{\partial^2 U}{\partial r^2} + (1/r)\frac{\...
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### Are the electrons at the centre of the Sun degenerate or not?

Trying to find an answer to this question, I came across two different methods of determining whether electrons at the center of the sun are degenerate or not. The first method, used here, calculates ...
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### How do we measure thermal energy?

My textbook says "The amount of thermal energy is found by measuring the temperature of the substance." However, how is this true? Temperature measures only the average kinetic energy of the particles ...
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### Is air infiltration a type of convective heat transfer (convection)

I have a building / physics question... A major source of heat loss in homes and buildings is infiltration through cracks (warm air from inside seeping out). Wondering if this falls in the category ...