The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:
ρ
=
m
V
{\displaystyle \rho ={\frac {m}{V}}}
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.
For a pure substance the density has the same numerical value as its mass concentration.
Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure.
To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one relative to water means that the substance floats in water.
The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.
The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.
Hi everyone,
there's something that I can't comprehend: when a homogeneous is in a conservative and non-uniform in module electric field polarization expression is given by P=ε0χE. Supposing the most general situation there's: divP=ρp where ρp is the polarization charge density in the...
Homework Statement
In the picture at points A and B are two thin parallel wires, where traveling currents are 15 A and 32 A to opposite directions. The distance between wires is 5.3 cm. Point's P distances from A and B are the same. Calculate the magnetic flux density at point P.
Homework...
((((As a correction dissipation function in picture should have square of divergence of U))))
Hi, first of all I am aware that we have to discretize the non linear navier stokes equations to reach the almost exact solution, and pressure based or density based algorithms are deployed for that...
With regard to the real number system, what is the importance of the Archimedean property and the property that the rationals are dense in ##\mathbb{R}## (which is a consequence of the Archimedean property)?
Related to this, what is the most general structure for which the Archimedean property...
I have the problem of making "at home" or almost, a measure of a laser's pulse energy for unit area of the target: those kinds lasts for ~ tens of milliseconds, up to some hundreds of ms and I should be able to verify that this energy "density" doesn't go beyond 40 J/cm^2 for a single pulse...
A solid sphere has surface charge density, Rho (r)
Rho(r) = k 1 ( 0 < r < a)
k2 x ( a < r < R)
2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R <
The attempted solution and the question with the diagram is attached below
Could the answer be verified...
Hi all, I have the following query:
I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to...
Hi everybody!
I need to compute a C++ program for solve Schrodinger equation and calculate nuclear density.
My nucleus is made up of only neutrons immersed in a potential of a harmonic oscillator.
Schrodinger equation is:
$$[-\frac{\hbar^2}{2m}\triangledown^2+V_{HO}(r)]\psi=E\psi$$
with...
Homework Statement
A sphere of radius R carries charge Q. The distribution of the charge inside the sphere, however, is not homogeneous, but decreasing with the distance r from the center, so that ρ(r) = k/r.
1. Find k for given R and Q.
2. Using Gauss’s Law (differential or integral form)...
According to [Dark Energy and the Accelerating Universe](https://ned.ipac.caltech.edu/level5/March08/Frieman/Frieman5.html) quantum field theory says that the energy density of the vacuum, ##\rho_{vac}##, should be given by
$$\rho_{vac}=\frac{1}{2}\sum_{\rm...
Imagine a container containing water up to 100cm of its height then I dip a cube of plastic in the water on depth of 75cm. We all know it will float because of its less density, but if we go with Pascal Law, The pressure/force applied by the water above the cube is more than than the buoyant...
Homework Statement
Homework EquationsThe Attempt at a Solution
In the region |z|<1 ,
E(z) = -dV/dz = 10zk
This means there is a variable electric field in the region -1<z<1 .In the +z region it is directed in the +z direction and vica versa .
For finding the charge density in the region...
<Moderator's note: Two threads on the same topic merged in order to have arguments and sources at one place.>
Can antimatter-matter be used as a fuel for a rocket?
There are various problems for anti-matter to be used as a fuel as it produces a lot of gamma rays. Gamma rays are not healthy to...
Why is the rough diamond in the following video held by a wire from above? Is it just so it will be easy to take the rock out of the water glass or is it to prevent the diamond from sinking to the bottom? If it is to prevent the diamond from sinking to the bottom, what is the reason for that ...
Homework Statement
A current of 1600A exist in a rectangular (0.4 x 16 cm) bus bar. The electrons move at an average velocity of v. If the concentration of electrons is 1029 per cubic meter, and they are uniformly distributed, what is v?
Knowns
Current (i) = 1600A = 1600 x 1018 aA
Charge per...
Homework Statement
This question concerns the resistance wire Nichrome.
''Nichrome is an alloy of nickel (80%) and chromium (20%).
The density of Nichrome is 8.56 g cm^-3.
Diameter/mm ------------------------->1.219 -- 0.914---0.711----0.560------0.457-------0.315
Current carrying...
Homework Statement
The following data concerning a constantan resistance wire is taken from a catalogue: ''Diameter/m = 5.6 x 10^-4, Resistance per meter = 1.947 ohms, Resistance per Kg = 913 ohms''.
Use the data to determine the density of the constantan wire in kg m^-3.
Homework Equations
V=...
The problem:
$$\mathcal{L} = F^{\mu \nu} F_{\mu \nu} + m^2 /2 \ A_{\mu} A^{\mu} $$
with: $$ F_{\mu \nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu} $$
1. Show that this lagrangian density is not gauge invariance
2.Derive the equations of motion, why is the Lorentzcondition still...
Homework Statement
from the lagrangian density of the form : $$L= -\frac{1}{2} (\partial_m b^m)^2 - \frac{M^2}{2}b^m b_m$$
derive the equation of motion. Then show that the field $$F=\partial_m b^m $$ justify the Klein_Gordon eq.of motion.
Homework Equations
bm is real.
The Attempt at a...
Hi,
I have a blog oriented on computational physics: https://compphys.go.ro For many posts I have a GitHub project. Lately I started some DFT oriented ones, the latest being a DFT (with plane waves basis) project for a 'quantum dot'.
Currently I started working on a project that will use the...
Homework Statement
Hello, I am trying to find the equations of motion that come from the fermi lagrangian density of the covariant formalism of Electeomagnetism.Homework Equations
The form of the L. density is:
$$L=-\frac{1}{2} (\partial_n A_m)(\partial^n A^m) - \frac{1}{c} J_m A^m$$
where J...
Homework Statement
A parallel plate capacitor is made of two flat horizontal conducting plates in a vacuum, each of area A, separated by a small gap. One plate carries a total charge 2Q, the other a total charge −Q. Find the surface charge densities on the four horizontal metal surfaces in...
Homework Statement
Q: A particle is in a linear superposition of two states with energies: ##E_0##& ##E_1##
$$|\phi>=A|E_0>+\frac{A}{\sqrt{3-\epsilon}}|E_1>$$
(a) What is the value of A ? Express your answer as a function of ##\epsilon##
(b) Use your expression to plot A vs ##\epsilon##
(c)...
This is kind of a random question. Is there a point that a substance density will max out? Or in other words that it cannot be compressed any further no matter the energy you add to the system?
Homework Statement
A tank of constant volume V contains air at an initial density pi. Air is discharged isothermally from the tank at a constant volumetric rate of Q (with SI units of m^3/s). Assuming that the discharged air has the same density as that of the air in the tank, find an...
Homework Statement
A semi-infinite (infinite in y and z, bounded in x) slab of charges carries a charge per unit volume ##\rho##. Electric potential due to this slab is a function of horizontal distance, x from the center of the slab. It is linear for ## x \lt -1m## & ## x \gt 1m##, and is...
Homework Statement
An E field with f = 2.45*10^9 Hz passes through a material with the following properties
e_r = 10
u_r = 1
sigma = 1 (S/m)
The Incident E field has peak magnitude of 300 V/m at the air to surface boundary.
(a) *solved* Find the incident power density at the material...
Hi, I'm studying the "Child Langmuir law". We have a grounded cathode that is an infinite plane with free electrons, and an anode with a positive voltage V. The text says that the current density J is constant between the two plates for the "Charge conservation principle". I was not able to...
Hey! :o
Let $X_1, X_2, X_3$ be i.i.d. with $X_1 \sim U[0, 1]$. I want to determine the density of $S=X_1+X_2+X_3$ using the convolution formula.
I have done the following:
Since $X_1, X_2, X_3$ are i.i.d. we have that they are independent identically distributed random variables. Since $X_1...
If mass of a particle is less than the vacuum energy density.. what would happen.. is this possible (also for some dark matter species)?
How about photons.. are they more or less than the vacuum energy density?
And what exactly is the value of vacuum energy density?
Dear Everybody,
A 2.80 kg steel gas can holds 20 L of gasoline when full. What's the average density (in kg/m^3) of full gas can, taking into the volume occupied by steel as well as by gasoline?
Work:
Given
the mass of the steel gas can= 2.80 kg
The Total Volume of Gas can= 20.0 L
The...
Good day all!
I've got a granular mixture of PLA, ABS, HIPS, and PETG with a particle size of about a quarter inch, and I'm trying to isolate each polymer from the mix. PLA and PETG have densities of about 1.27g/ml, and ABS and HIPS have densities of around 1.06g/ml. I think a weighted solution...
Hi,
I'm trying to understand Einstein's field equations conceptually, does it describe space density in a region of space by any chance? Like there is more space in this region compared to this other region. Thanks.
A overflow container that its overflow level is $100$ $cm^3$ has $80$ $cm^3$ water. When a stone that is $120$ $g$ is being dropped into the overflow container, the water increases $10$ $cm^3$.
How to find the density?
I currently don't have any idea about it.
Homework Statement
How many free electrons are there in the CB? Diamond has a bandgap of ##5.5##eV.Assume the material is at room temperature and that there are ##2 \times 10^{22}## cm##^{-3}## electrons in the material. What does this mean for their use in semiconductor devices?
Homework...
I have a problem here. I don't get why the stagnation pressure equal the height of the water in the pitot tube.
The liquid manometer is easy. We analyse the forces on the horizontal contact surface of the tube and the liquid manometer so P1 = Density * g * h
However I fail to analyse the...
I was watching a movie called Everything and Nothing. It got me thinking. For the sake of argument pretend that you could make the sun pop in and out of existence. If you were to measure the distance between two points on the other side of the solar system with no sun, then if the sun were to...
Homework Statement
An infinitely long cylindrical capacitor with inner radius a and outer radius b carries a free charge per unit length of ##\lambda_{free}##. The region between the plates is filled with a nonmagnetic dielectric of conductivity ##\sigma##. Show that at every point inside the...
If i have Energy Density (U) -> U.Area= F but F.Area = pressure (p) but p must be U . I'm confused! In which cases we can say that energy density is pressure?
I'm currently carrying out an experiment with Fraunhofer diffraction. It involves shining a laser beam through neural density filters, a lens and a diffraction grating, to create a diffraction pattern which is then picked up with a CCD camera, to find the intensity of the maximal peaks.
However...
Homework Statement
Consider an infinitely long one dimensional conducting wire with a homeogenous charge density ##\lambda##, running along the central axis of an infinitely long cyclindrical glass casing of radius b (glass is a dielectric material). Calculate:
a) The displacement vector...
I noticed the other day something odd in how we use Electric and Magnetic flux.
The definitions I refer to are magnetic flux density (B), magnetic flux intensity (H), electric displacement field (D) or Electric field density (D) and electric field (E):
B = μH
ΦB = B*Area
&
D = εE
ΦE = E*Area...
Hi guys,
got a little problem I'm currently working on and looking for some input/sanity check.
Firstly i have a round tank within a round tank both with open tops, the inner tank is suspended within the outer tank such that there is a gap between both tanks bottoms faces, the inner tank open...
Hey all!
I am prepping myself for a quantum course next semester at the graduate level. I am currently reading through the Cohen-Tannoudji Quantum Mechanics textbook. I have reached a section on the density operator and am confused about the general concept of the operator.
My confusion stems...
Hi,
I am attempting the following question:
1. Homework Statement
If the extinction in the infrared K-band (filter central wavelength = 2.13 micrometres) is 10 times less than it is in the optical V-band (filter central wavelength = 550 nanometres), what affect would a cloud of Av = 3 have on...
So I am studying Gauss's law and I am a bit confused about something. If I am asked to compute the volume or surface charge density of a solid perfectly conducing sphere with a charge Q and radius r, what is being asked of me? Am I just being asked to compute the volume of a sphere and multiply...
Homework Statement
A city surrounds a bay as shown in Figure 1. The population density of the city (in thousands of people per square km) is f(r, θ), where r and θ are polar coordinates and distances are in km.
(a) Set up an iterated integral in polar coordinates to find the total population...
Homework Statement
Find the z -coordinate of the center of mass of the first octant of a sphere of radius R centered at the origin. Assume that the sphere has a uniform density.
Homework Equations
Mass = Integral of the density function
Center of mass for z = Integral of density * z divided...
Hello all; I am new in this forum, currently in High School.
For some time now, I have been looking online for a relationship between temperature and magnetic flux density of a ferromagnet; below the Curie point. However, I can't seem to find any relationship or formula. Do any of you know...