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.
Homework Statement
Assume that the pressure p in a star with spherical symmetry is related to the density \rho by the (distinctly unrealistic) equation of state p= \tfrac12 k\rho^2, where k is a constant. Use the fluid equilibrium equation obtained in Problem 23 to find a relation between \rho...
Homework Statement
It is known that the potencial is given as V = 80 ρ0.6 volts. Assuming free space conditions, find a) E, b) the volume charge density at ρ=0.5 m and c) the total charge lying withing the closed surface ρ=0.6, 0<z<1
Homework Equations
E[/B]=-∇VThe Attempt at a Solution
(this...
Homework Statement
An experiment probes a coherent process and the receiver is coherent. The autocorrelation function and the spectral density function are estimated and transformaed into atmospheric parameters. See Table 1 below
1) Calculate the maximum velocity (in m/s) that may be...
Homework Statement
Two large non-conducting plates of surface area A=.025m^2 carry equal but opposite charges Q = 75microC. What is the energy density of the electric field between the two plates.
Homework Equations
I wrote the equations on my attempt. This was a multiple choice problem...
I always has the impression that the density of the universe is infinite at the singularity because its just amount of stuff divided by volume and if the distance between stuff is 0 then the volume is 0. So divide by zero and you get infinity. But I have been told by others that dividing by zero...
Homework Statement
A metal wire is given a ceramic coating to protect it against heat. The machine that applies the coating
does not do so very uniformly.
The wire is in the shape of the curve
The density of the ceramic on the wire is
Use a line integral to calculate the mass of the...
In the situation consisting of a steady current of 1A in an arbitrary closed path, what would the consequences be for the electric field if the drift velocity was non-uniform along the path due to non-uniform carrier density?
This would be a case of a "uniform" 1 amp, but where the charge...
Hello!
Let's consider again a system of atoms with only two permitted energy levels E_1 and E_2 > E_1. When electrons decay from E_2 level to E_1, they generate a photon of energy E_{21} = E_2 - E_1 = h \nu. The number of photons (per unit frequency, per unit volume) emitted by such a system in...
For a standard solenoid, I've found that
B=μnI
where
μ = permeability of the core (4π×10^-7 for free space)
n = number of coils
I = current
Firstly, is the permeability of soft iron 0.08, as I found?
Primarily, however, I'm wanting to know if this still applies for a mutual induction apparatus...
In any simple carboxylic acid there are two oxygen atoms then i have a confusion that which oxygen has more negative charge on it or which one has the most electron density on it?
Is it possible to calculate the average number of Cooper-pairs, existing at any given moment, per cubic centimeter of niobium (or YBCO), at their critical temperatures? I realize that Cooper pairs form and dissolve continuously, and constantly change partners, so perhaps its not easy to...
In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...
i am trying to figure out the relationship between diameter of a drop of liquid, its density and its shape. Can somebody explain to me the following two lines?
From the view point of quantum field theory how does one describe the electromagnetic energy density between the plates of a charged capacitor?
Thanks!
Hello,
I am an electrical engineer rather than a physicist, however, I am trying to understand the physics of a twin wire transmission line in terms of the charge and current density. Let's say we have a lossless, infinite length, twin wire transmission line, a step current is induced into the...
Homework Statement
I'm confused about the following kind of situation. Consider a block of density ##\rho_b##, mass ##M_b## and section ##S_b## that floats on a liquid of density ##\rho_l##, in a tank of section ##\mathcal{S}##. On the block there are some objects (all equal), of density...
The following derives the relation that for a blackbody radiation the energy density is proportional to the energy emitted per unit area over unit time.
The average energy density ##d\psi## is obtained by dividing the radiant energy ##dE## received by the surface ##dB## in 1 second by the...
Hello,
I'm stuck with this exercise, so I hope anyone can help me.
It is to prove, that the density of states of an unknown, quantum mechanical Hamiltonian ##\mathcal{H}##, which is defined by
$$\Omega(E)=\mathrm{Tr}\left[\delta(E1\!\!1-\boldsymbol{H})\right]$$
is also representable as...
When I read that conditions were such and such 1 to .05 seconds after the big bang, is that duration somehow longer than 1/2 second is now (maybe because of the difference in density or like the twin paradox?)?
Can any expert help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system.
$$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2}) & cos(\frac{\alpha}{2})+sin(\frac{\alpha}{2}) \\ 1 & 1 &...
Homework Statement
I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac notation, Ket Bra.Homework Equations
[/B]
My problem here I want to know the...
It seems by this paper that there are more black holes than expected, so what is the expected density of black holes in the nearby universe?
arXiv:1606.04996 (cross-list from gr-qc) [pdf, other]
Constraining modified theories of gravity with gravitational wave stochastic background
Andrea...
Homework Statement
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...
Homework Statement
A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif
Its circular surfaces are horizontal. What effect will the...
Homework Statement
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...
Hi, in gravitational theory the action integral is: I = ∫( − g ( x))^1/2 L ( x) d 4 x, but I do not know why there is a square root -g . Could you give me the proof of this integral? I mean How is this integral constructed? What is the logic of this? Thanks in advance...
Homework Statement
A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.53 hours. What is the density of the planet? Assume that the planet has a uniform density.
Homework Equations
T^2=(4pi^2r^3)/GM
V=4/3piR^3
Density= Mass/...
Hi,
I know how to calculate density of states for both cases, but it is not clearly to me how I can go from 3D case to 2D. I have energy from infinite potential well for 3D
$$E=\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{l_x}+\frac{n_y^2}{l_y}+\frac{n_z^2}{l_z})$$
let make one dimension very small...
Hey guys, I just wanted to check if my method for solving this problem is correct.
1. Homework Statement
Consider an annulus with inner radius R1 and outer radius R2. The mass density of the annulus is given by σ(r)=C/r, where C is a constant. Calculate the total mass of the annulus.
Homework...
I am trying to calculate the flux density of an air gap in an electromagnet.
I am following this page that calculates the flux density in a C core with an air gap.
My confusion is that I am using 50Hz AC instead of DC I have control over the voltage amplitude since I would be using a variac to...
Hello!
When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components
k_x = \displaystyle \frac{\pi}{L_x}p
k_y = \displaystyle \frac{\pi}{L_y}q
k_z = \displaystyle \frac{\pi}{L_z}r...
Had an argument with a few guys at the gym today. I told them that loading a barbell with 100 on each side instead of 2 45s and a 10 causes more pressure on your spine. This example is in reference to someone performing a low bar squat in which the bar has contact points across the entire back...
Its said that if there are different pocket universes made by inflation then this solves the alleged fine tuning of dark energy. My question is this: can the idea of different values for the vacuum energy density in these different pockets be derived from quantum field theory or does it need...
It says in Susskind's TM:
##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}##
with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?
So if a car were to somehow have its density lowered by lowering the mass, but keeping the volume the same, would the car be more damageable and breakable than it was before, or would that depend on something else other than density?
How is a top gate used to change electron density in 2D semi conductors?
I get the principle, you are just shifting the chemical potential by some voltage so that there are more or less electrons in the specific bands. But how is it physically done?
Thanks.
Hi,
I'm taking an undergrad course in Electromagnetism and Optics, and in the lecture notes it reads:
"Consider the formal equation ε0D⋅E = 1 ... that must be obeyed for waves traveling in different directions as defined by the wave vector k but with a given energy density."
Could anyone help me...
Hi,
For someone who's familiar with LC's:
How to derive the expression for free energy density of an hybrid aligned LC cell? what should be the vector for the director?
I already familiar with the cases of splay and bend cell but couldn't understand how to derive it to the case where the cell is...
Homework Statement
Given a sphere with radius R, centered at (0,0,0), it's dipole density given as ##P\left(\vec{r}\right)=\alpha\left(R-r\right)\hat{z}## where r is the distance from the center of the ball.
I'm required to find:
Bound charge density inside the sphere, bound charge density on...
I want to use the equation:
Fr='gamma'*distance from centroid*Area
but the example is showing density in N/m^3
while I only have the density in kg/m^3
Does this mean I have to multiply it by 9.81 to get the right answer?
Thanks.
Hello, let be ##x \in \mathbb{R} - \mathbb{Q}##, do we have de density of ##\{nx - \lfloor{nx} / n \in \mathbb{N}\}## in ##[0; 1]## please?
I think yes but it's just an intuition : if I take a and b in ##[0; 1]## with a < b, I have an irrationnal between them let call it c but I don't know...
I have a Stats exam on Wednesday and while I thought I was quite well-versed, I've gone back over to the very basics only to find myself confused at what should be introductory.
Suppose I have a continuous random variable modeled by a probability density function: $$f(x)=2x$$ Obviously the...
The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law essentially uses the fact that, if ##\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3##, ##\boldsymbol{J}\in C_c^2(\mathbb{R}^3)##, is a compactly supported twice continuously differentiable field...
Homework Statement
A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]Homework Equations
For canonical ensemble
##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}##
In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|##
The...
I'm doing a question relating to the pressure inside on object submerged in water. Here is the question:
A tube, height 1.2m, is submerged vertically in the ocean where the waters density is 10^3 kg/m^3. A diver initially holds the tube vertically directly on top of the water. He then dives to...