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.
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(This is a long problem but I think the question is not hard.)
Determining the star density from star counts is tough, but estimating counts from a density law is simpler. In practice, this method of fit-ting observed number counts to an assumed density law is becoming a...
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Hi!
I really need help with finding time- dependent continuity equation for electron densities in the atmosphere. I've tried to solve it without any success. My question is if someone can give me a good link/link or equations that I can start with.
Homework Equations
See...
Homework Statement
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Consider a long chain of mass m and length L suspended from a tall ceiling. Like any string if one end is disturbed waves will travel along the string. However, the tension in the string is due to its own weight and is not uniform. As such the speed of the wave will be...
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Homework Equations
See below
The Attempt at a Solution
\begin{align}
\begin{split}
p(x) = C \ x \ exp(-x/ \lambda)
\end{split}
\end{align}
If $p(x)$ is a probability density function on the interval $ 0 \textless x \textless + \infty $ , then it follows...
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I want to find the mathematical proof to show that the density of an object changes with thermal expansion. My professor showed this in class and it was horribly wrong because he let a few things out. The book I'm reading showed it in 4 steps and left out a lot of the crucial...
It is easy to show that when you have a quantum system, let's think for example in electrons in a metal, then there appears summation over electron states of the form, e.g. for the energy for a free electron gas at T=0K:
##E=2 \sum_{k\leq k_f} \frac{\hbar^2}{2m}k^2##
Where ##k_f## denotes the...
Hello,
I am new to the forum, so I am directly stating my questions.
1)What determines the density of states of Phonons in a semiconductor?
2)Does degeneracy of semiconductors depend only on doping?
Thanks
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in this notes , i was told that the PV=mRT , why ? shouldn't PV= NRT , N=number of moles ? it should be PV = m/M (RT) , right ?
Homework EquationsThe Attempt at a Solution
Hi, I've been given a list of heights and corresponding densities of air at these heights. I'm trying to find an expression for the variation of density with height. From the data, it looks like the density would be equal to some kind of logarithmic relationship? However, I'm not too sure how to...
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For the observation of quantum mechanical Bose-Einstein condensation, the interparticle
distance in a gas of noninteracting atoms must be comparable to the de Broglie
wavelength, or less. How high a particle density is needed to achieve these conditions
if the atoms have mass...
Hi, I'm looking for a liquid that is nontoxic, high transmittance, has a specific gravity higher than 1.3.
Here is the catch. I'm using it to separate resin, so it can not dissolve or react with resin.
there was a similar topic on high density fluid on other forums, but I'm using it...
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Consider the diffusion of a drop of ink in a water vase. The density of the ink is ## \rho (\vec{r}, t) ##, and the probability ##P(\vec{r}, t)## obeys the diffusion equation. What is the relationship between ##\rho (\vec{r}, t)## and ##P(\vec{r}, t)##?
Homework...
Homework Statement
Let’s introduce an imaginary atom which can replace the silicon atom and
generate one mobile electron. What is electron density when all silicon atoms are replaced by this imaginary
atom
Homework EquationsThe Attempt at a Solution
I have tried looking for a formula to...
Five days ago, I filled a glass 2L bottle about halfway with litchis, then filled the bottle with water till the end and sealed it with its cap. I was curious to see how it decomposes in there. This morning, about 1/7th of the water was lying in a puddle around the bottle. I could see gas...
Hello,
I am wondering about the following action in a stator:
If the inlet angle in a stator is B, and the outlet angle is -B, what exactly is happening? Axial vlocity should be constant, and so should the relative velocities except being mirrored and i am asuming infinitely thin blades.. Can...
I usually come across expressions for the Stress energy tensor showing them as three densities (normally over a space-like slice.
In wikipedia's article on the spin tensor, they clearly (it does not appear to be an error) both write about and express the components of the stress energy tensor as...
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We fully submerge an irregular 3 kg lump of material in a certain fluid. The fluid that would have been in the space now occupied by the lump has a mass of 2 kg. a) When we release the lump, does it move upward, downward, or remain in place? b) If we next fully submerge it in...
I observe that electric arc forms a curve. I think that this is because electric arc is extremely hot and hot air goes up because it has less density. So if electric arc occur at 0 gravity would it be straight?
from wikipedia https://en.wikipedia.org/wiki/Electric_arc
Thank you.
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If you have a body that weighs 100 N dipped in oil that has density equal to 0.8 g / cm³. This same body when immersed in water begins to weigh 60 N. How do I find the density / specific body mass?
Homework Equations
Solution= 1,3 g/cm³
The Attempt at a Solution
Already...
Is it possible to work out analytically how the mass density profile ρ(r) of a ball of gas (spherically symmetric) evolve with time given the initial profile ρ0(r)? The assumption here is that the particles collapse only under the influence of gravity. I thought of this question in the process...
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I am trying to solve Problem 2.45 in Electrodynamics by Griffiths, however, my answers were different from those in the book, I am suspect I got a missing step but I could not find it, so here is the Given Problem
Find the charge density \rho given by a potential...
How does insulator's density affect its thermal conductivity?
For example, considering such insulators as rock wool, It seems that the thermal conductivity should increase with an increase in density (due to elimination of 'air pockets'). However, experimental results, in many cases, look more...
A receptacle has a mass of 3 kg when it is empty, 53 kg when it is filled with water, and 66 kg when it is filled with glycerin. Calculate the relative density of glycerine.
I know the formula to find out the relative density.
d= absolute density / reference density ( 1000kg/m3)
All,
I am wanting to see why charge density divided by e nought is equal to F/q and V/d. Unit cancellation makes it easy to equate F/q = V/d, but why is charge density alone enough to be equal to the electric field? I feel like something is missing here but I can't reconcile it nicely in my...
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What is the diameter of a copper sphere that has the same mass as a 9.00 cm× 9.00 cm× 9.00 cm cube of aluminum?
Density of Aluminum = P(al) = 2.70g/cm3
Density of Copper = P(cu) = 8.96 g/cm3
Volume of Aluminum Cube = Vcube = 729 cm3
Homework Equations
Volume of a Sphere =...
Hello! I am new to this forum, but I'll give it a shot.
It is my understanding that photons have no mass- but that light is still pulled by the gravity of a black hole. How can something without a mass, and therefore, gravity, be pulled by the gravity of another object? Any insight would be...
There is something that I don't quite understand or want clarification. See John Wheeler article "100 years of the quantum"
http://arxiv.org/pdf/quant-ph/0101077v1.pdf
refer to page 6 with parts of the quotes read
"so if we could measure whether the card was in the alpha
or beta-states, we...
In another thread
https://www.physicsforums.com/threads/why-does-the-universe-have-no-net-charge.843865/page-2#post-5326092
I was amazed to learn the following from a post by bcrowell:
"You can't get the total mass of the system by adding up the masses of all its parts."
The reason for this is...
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A column of water 40 cm high supports a 30 cm column of an unknown liquid.What is the density of the liquid?
Homework EquationsThe Attempt at a Solution
As per the instruction of the teacher I equated their pressures.
h1ρ1g=h2ρ2g. And hence arrived at the...
Hello
Lastly I was thinking a lot about electron density definition. It is not intuitive for me and I'm looking for any mathematical tool that could explain it to me more. My friend told me about idea to derivate it from propability density function using Dirac delta distribution. I'd like to...
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1.0 mA proton beam accelerated through potential difference of 1 keV.
Determine the volume charge density of the beam after acceleration assuming uniform current distribution within diameter of 5mm, with zero current outside of this.
Particle starting from rest.
Final answer...
Hello,
What is the energy dispersion relation and density of states for graphen near the Dirac point ? I am looking for a proper graph illustrating these properties.
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A two-dimensional circular region of radius a has a gas of particles with uniform
density all traveling at the same speed but with random directions. The wall of the
chamber is suddenly taken away and the probability density of the gas cloud subsequently
satisfies
$$...
I asked this once before, but forgot the answer.
I know the difference between the two. I would like to know why S.G. is even relevant since it seems to give the same answer as density.
Ex. Density of a fluid is 10 g/cm3 and density of water at 4C is 1g/cm3 so the S.G. of the fluid is 10 (no...
Fermi's golden rule contains a term that is the density of the final states ##\rho(E_{final})##. For my problem we have no time depending potentials so that's the same as ##\rho(E_{initial})##.
If I understand the definition of ##\rho## correctly, it's the number of states in an interval...
Dear all,
I am trying to understand the physics behind the "number density" formula given by Weinberg.
Is there anyone who can explain these parameters to me:
1- "Initial fluctuation strength":
\begin{equation} \rho_1= \lim_{t \to 0}\frac{\Delta \rho_M^3}{\bar{\rho}^2_M}\end{equation}
However...
Hi
I'd like to ask you about interpretation of electron density definition. According to the "Handbook of Molecular Physics and Quantum Chemistry" it goes like:
##\rho (\textbf{r})=N \sum_{\sigma_1}^{\sigma_N} \idotsint_{\mathbb{R^3}} |\psi_V (\textbf{r}_1, \sigma_1;\dots...
First, we know for every wave function
$$p(x)=\psi(x)^*\psi(x)$$ indicates the probability density of a particle appearing at the point x.
So if we calculate $$P=\int _M p \text{d}x$$ this gives the probability of the particle appearing in the range M.
On the other side, I was thinking about...
For a state |\Psi(t)\rangle = \sum_{k}c_k e^{-iE_kt/\hbar}|E_k\rangle , the density matrix elements in the energy basis are
\rho_{ab}(t) = c_a c^*_be^{-it(E_a -E_b)/\hbar}
How is it that in the long time limit, this reduces to \rho_{ab}(t) \approx |c_a|^2 \delta_{ab} ?
Is there some...
Spacetime shrinks in a gravitational field. As I understand it, objects falling into a black hole will appear to contract in size and run slower as they approach the horizon. This is similar to how things contract and slow down when traveling close to the speed of light because they are...
I'm doing some research for a sci-fi story that I'm writing and hoping that some of you chemists can help me answer a quick question about the material of a hypothetical distant planet.
If a distant planet were three times the size of Earth with the same gravitational pull, what would the...
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Hi everyone. I watched a YouTube video earlier today which said that sound waves travel faster in more dense mediums. For example, sound travels faster in water than it does in air.
However, on this webpage http://www.physicsclassroom.com/mmedia/waves/ltm.cfm it says that...
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Determine ##P(X<Y|x>0)##
Homework Equations
X and Y are random variables with the joint density function
$$
f_{XY}(x,y)=
\begin{cases}
4|xy|,-y<x<y,0<y<1\\
0,elsewhere
\end{cases}$$
The marginal densities are given by
$$
f_X(x)=2x\\
f_Y(y)=4y^3
$$
The Attempt at a Solution...
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So I have two 1/2 spin systems A and B in a singlet state |\psi > = \frac{1}{\sqrt{2}} ( |+-> - |-+> ) . The question is: If I measured B and got S_{Bz} = 1/2 . What will I measure on state A on z axis?
Homework EquationsThe Attempt at a Solution
The answer I think is...
I searched for, but could not find any name or published value for a constant (with units m-3 K-3) which when multiplied by temperature (in degrees Kelvin) cubed gave the corresponding photon density (in m-3).
Does anyone know of such a constant with a published value?
I calculated a value, but...
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I have a free Brownian particle and its coordinate is given as a function of time:
And its first moment, or mean, is given as
But what kind of probability density was used to calculate this first moment?
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I know that the first moment is calculated...
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Not sure if this is the correct place to post so move if needed.
In a cylindrical conductor of radius R, the current density is givne by j_0 e^{- \alpha r} \hat{k}. Where ##\alpha## and ##j_0## are some constants and ##\hat{k}## is the unit vector along the z-axis.
...