The tag has no usage guidance.

learn more… | top users | synonyms (1)

1
vote
1answer
47 views

Kinetic theory of physics [closed]

$$E = (3/2) kT$$ For average kinetic energy of a molecule gas.The constant $k$ does not depend on the type of molecule. Can this result be true for both hydrogen and chlorine?
1
vote
1answer
24 views

Degrees of freedom for custom made finger

I'm designing a 3D printable prosthetic hand. Each finger has 3 joints. The first 2 joints let the finger only move in the vertical (y) direction. The final joint is like a ball and socket joint ...
1
vote
0answers
30 views

General relativity degrees of freedom — simplified version?

I'm afraid my question may be too general, but I would like to ask how I could find out the degrees of freedom in a given tensor. I have had this question since I started studying GR. At first, I ...
3
votes
1answer
97 views

Rigorous definition of degrees of freedom

According to this Wikipedia article, the definition of degrees of freedom is: The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its ...
1
vote
1answer
42 views

Why do $\psi_a$ and $\bar{\psi}_{\dot{\alpha}}$ represent two different degrees of freedom?

I am taking a course in QFT and I've been introduced to the concept of left-handed (undotted) and right-handed spinors (dotted). I know that left-handed spinors are associated with the irreducible ...
1
vote
1answer
43 views

Why does a system whose equations of movement are $\lambda^2U^{\alpha} + \partial_{\mu}F^{\mu \alpha} = 0$ have three degrees of freedom?

I'm trying to understand the solution of a problem where I have to study a field ($U^\mu$) which Lagrangian is: $$\mathscr{L} = - \frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \frac{1}{2} \lambda^2 U_{\mu} ...
0
votes
1answer
37 views

Prove that $n$ degrees of freedom leads to $n$ normal modes

I have probably missed that during my studies. I intuitively know (but then I might be wrong in some detail, that's why I am asking), that $n$ degrees of freedom in oscillating system leads to $n$ ...
0
votes
0answers
29 views

Find the Kinematic degrees of freedom of the following contraption

In the above mechanism it is required to find the generalized coordinates to write equation of motion of the MDOF system. I just want to ask how do we actually approach such a problem? How to ...
-1
votes
1answer
34 views

At what temperature does the vibrational degree of freedom becomes significant for an ideal diatomic molecule?

For ideal diatomic molecules such as $\text{H}_2$, $\text{N}_2$ and $\text{O}_2$, at what temperature does the vibrational degree of freedom significantly contributes to the calculations such as that ...
1
vote
1answer
47 views

State counting in the d = 1+2, $\cal{N} = 2$ vector multiplet

The question is from Box 8.2, page 282 of the book "Gauge Gravity Duality" by Ammon and Erdmenger. The link to the specific page from Google Books is here. According to the authors, a $\mathcal{N} = ...
2
votes
1answer
48 views

Matching bosonic and fermionic degrees of freedom in Wess-Zumino Lagrangian

In Wess-Zumino model, supersymmetric Lagrangian in addition to the ordinary complex scalar field $\phi$ contains auxiliary field $F$ (also complex scalar) to match the degrees of freedom of the Weyl ...
0
votes
0answers
28 views

How many degrees of freedom to diagonalize the metric?

In A. Zee's Einstein Gravity in a Nutshell, he starts with the following expansion of the metric at some point $P$ of a Riemannian manifold, with coordinates $x^\mu$ that have the origin at $P$: $$ ...
2
votes
0answers
98 views

Off-shell degrees of freedom of a massive vector field [closed]

A gauge boson is described by a vetor field $A_{\mu}$, so in four dimensions $\mu$ runs from $0$ to $4$ and thus $A_{\mu}$ has $4$ degrees of freedom (d.o.f), but the gauge invariance ...
1
vote
0answers
76 views

What happens to Goldstone bosons in the Higgs potential after symmetry breaking?

When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), ...
0
votes
4answers
77 views

For a diatomic molecule, what is the specific heat per mole at constant pressure/volume?

At high temperatures, the specific heat at constant volume $\text{C}_{v}$ has three degrees of freedom from rotation, two from translation, and two from vibration. That means ...
2
votes
1answer
497 views

Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...
0
votes
1answer
80 views

The “potential energy” degree of freedom?

I'm reading Schroeder's "An Introduction to Thermal Physics" and he mentions the vibrational degrees of freedom of a diatomic molecule: A diatomic molecule can also vibrate, as if the two atoms ...
0
votes
1answer
61 views

Rotational/spin degrees of freedom for a monoatomic gas in free space [duplicate]

How many degrees of freedom does a monoatomic gas have? According to my Thermal Physics textbook, there are $3N$ degrees of freedom for $N$ particles because the particle is free to move in the $x$, ...
0
votes
0answers
85 views

What is the degrees of freedom of metric tensor?

As $g_{\mu\nu}$ can be taken to be symmetric, it contains 10 functions of spacetime in 4 dimensions. But, why we call these 10 functions as the degrees of freedom of the metric while they are the ...
3
votes
1answer
118 views

Do photons have six degrees of freedom?

Calculations involving pressure and volume relationships of photon gas during the cosmologic expansion of the universe posit an adiabatic cooling process with a heat capacity ration of 4/3. This ratio ...
1
vote
0answers
62 views

Finding the configuration space and degrees of freedom of spherical pendulum

Suppose we have a spherical pendulum tethered to the origin in $\mathbb{R}^3$ where the length of the rod is a time varying function $l(t)$. What is the configuration space of this system, and how ...
4
votes
3answers
699 views

Why do we say linear molecules only have 2 rotational degrees of freedom? Why does the third 'frozen' one not count?

It is possible to excite rotations around the axes perpendicular to the bond of a linear molecule. However, rotation around the axis along the bond of the molecule would require huge energies, due to ...
0
votes
2answers
117 views

Do rotational degrees of freedom contribute to temperature?

Recently I have come across a mathematical problem where I was said to calculate the temperature increase of certain mol of N2 gas confined in a room. However, I found that there was only ...
0
votes
3answers
156 views

Degrees of freedom of a two particle rigid system

We have two particles and the distance between them is fixed, let's suppose we know the coordinates of one particle (2,1) and other particle (x,2). So using distance formula (let's suppose the fixed ...
6
votes
1answer
99 views

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 ...
2
votes
1answer
93 views

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?
5
votes
2answers
250 views

Extra vibrational mode in linear molecule

When calculating the number of vibrational modes for a molecule, the formulas differ for linear $(n = 3N - 5)$ and non-linear $(n = 3N - 6)$ molecules, where $n$ is number of modes and $N$ is number ...
2
votes
2answers
264 views

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 ...
1
vote
1answer
129 views

Should the (On-shell) (2+1)d $N=2$ Chiral Multiplet Contain Two Scalars and Two Majorana Spinors?

In supermultiplets, the bosonic degrees of freedom and the fermionic degrees of freedom need to match in number. The number of degrees of freedom of a field corresponds to the number of independent ...
2
votes
1answer
64 views

Degrees of freedom of a point mass sliding on a rigid curved wire without friction

I am very new to the subject and am going through Structure and Interpretation of Classical Mechanics. One exercise asks to find the degrees of freedom of a number of systems, one of which is a ...
2
votes
1answer
163 views

Why does the Dirac equation reduce the fermionic degree of freedom by half

We know that in 4D a Dirac spinor has 4 complex components or 8 real components meaning 8 real off shell degrees of freedom (please correct me if I say something wrong here). When we go on-shell i.e ...
5
votes
2answers
820 views

Why energy at room temperature $= kT$ and not $(3/2)kT$ [duplicate]

I always see that a room temperature of $T=300\,\text{K}$ corresponds to an energy of $k_BT \approx \frac{1}{40}\,\text{eV}$. But shouldn't it be $\frac{3}{2}k_BT$ since the molecules in the air have ...
1
vote
1answer
458 views

Holonomic constraints and degrees of freedom?

Can we see that a constraint can decrease the degrees of freedom of a system if and only if it is holonomic. Either way please can you explain why?
1
vote
0answers
66 views

Proving the Virial theorem

Consider the expectation in the canonical ensemble defined by $$\left\langle x_i\frac{\partial \mathcal{H}}{\partial x_j} \right\rangle=\frac{1}{Z}\int d\Gamma x_i\frac{\partial ...
0
votes
1answer
44 views

Amount of unknown parameters in compressible Euler equations

I'm looking at this page for the compressible Euler equations. To me it seems, in the 1-dimensional case, there should be 3 unknowns: density, velocity, and pressure. This is because the energy $E$ ...
0
votes
1answer
161 views

Degrees of freedom in double Atwood machine?

Why the degree of freedom in double Atwood machine (one block on one side and a pulley with one block in its each side on other side) is 2 and not 1? According to the formula $s=3*n-m$; where ...
3
votes
1answer
437 views

Number $g(T)$ of relativistic degrees of freedom as a function of temperature $T$

Let us consider the total number of relativistic degrees of freedom $g(T)$ for particle species in our universe: $$g(T)=\left(\sum_Bg_B\right)+\frac{7}{8}\left(\sum_Fg_F\right)$$ Where the sums are ...
11
votes
2answers
615 views

In counting degrees of freedom of a linear molecule, why is rotation about the axis not counted?

I was reading about the equipartition theorem and I got the following quotations from my books: A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis ...
1
vote
2answers
1k views

Definition of generalised coordinates?

I think the definition of generalised coordinates is something along the following lines: A set of parameters that discribe the configuration of a system with respect to some refrence ...
0
votes
0answers
42 views

Ideal Bullet Block

What if in the experiment by Veritasium Bullet Block Explained, we used an ideal block and bullet, so that the collision is perfect elastic, and the bullet doesn't stick to the block after hitting it? ...
0
votes
1answer
49 views

Locally accessible dimensions of configuration space

I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ...
2
votes
2answers
130 views

What's the degree of freedom of this kind of matrix?

We first have a unitary matrix $$\{a_{ij}\}\quad(n\times n)$$ I know how to calculate its degree of freedom, which is $n^2$ if we consider a real variable as one degree of freedom. Now we have a ...
2
votes
1answer
76 views

Counting d.o.f. and gauge fixing $A_{\mu}$ and $\psi$ in $D$-dimensions

Setup: Let us assume we are in $D$-dimensional Minkowski space-time where $D=d+1$. Consider a free Abelian gauge theory. Then the electromagnetic field will satisfy $$\partial_{\mu}F^{\mu \nu}=0 ...
1
vote
1answer
74 views

Polarization in blackbody radiation

While doing some calculation in Statistical Mechanics of blackbody radiation from Huang's Statistical mechanics, I came across with the factor 2 which it says comes from two possible polarizations. ...
3
votes
0answers
207 views

Quantum vs classical degrees of freedom

It is sometimes stated that any classical underpinnings (rightly non-local) of a general quantum system are unrealistic or unphysical because these require exponentially more information to store what ...
2
votes
1answer
592 views

Degrees of freedom in Quantum Mechanics

If we look at a particle in classical mechanics, the degrees of freedom increase as its size decreases like the degrees of freedom of an atom is more than that of molecule, and subsequently, the ...
1
vote
1answer
373 views

Why is molar specific heat at constant volume of a monatomic ideal gas a constant?

I thought specific heat varies depending on the substance. Why is it always $(3/2) R$?
1
vote
0answers
77 views

Are there diffrent understandings of dimensions?

If people are talking about 4 or higher dimensions they are always pictured as space dimensions. But if you have have a look at the simplest definition of a mathematical dimension it only needs to be ...
3
votes
2answers
424 views

$E=kT$ or $\frac32kT$?

Basically, which is the correct formula for thermal energy, and is this the same as kinetic energy? My notes are pretty conflicting on this topic, and I'm getting pretty confused.
1
vote
1answer
79 views

Explicit Symmetry Breaking: Where do the additional d.o.f. come from?

Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive ...