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.
Hey everybody, :smile:
I have a joint density of the random variables ##X## and ##Y## given and want to find out ##P(X+Y>1/2)##.
The joint density is as follows:
$$f_{XY}(x,y) = \begin{cases}\frac{1}{y}, &0<x<y,0<y<1 \\ 0, &else \end{cases}$$
To get a view of this I created a plot:
As...
I am only asking about part (b)(i) and (b)(ii).
Below is the explanation for (b)(i).
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hi need help in physics HW:
given current density [J][/→]=[J][/0][x][/Λ]
and rotating frame with given surface vector:
$$ A^→ = A_0(cos(wt)x^Λ + sin(wt)y^Λ$$
in need to calculate I(t)
i tried
I = ∫J*dA
but i don't know i to technically do the math
please help me
Summary:: Is the magnetic flux density B constant? Is the magnetic flux constant?
I am working on a project design for Uni and I am stuck.
In a magnetic circuit is either the magnetic flux or the magnetic flux density B constant? This magnetic circuit has all different cross section areas and...
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Let...
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Hello,
I found this article. In equation (1) the authors wrote that the current operator is given by : ## - \frac{\delta H}{\delta A} ##.
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Thanks !
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hi guys
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and to...
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My issue is that I don't know how to...
Given a probability density distribution ##P(\vec{x})##, for what named distributions is the following true:
\begin{equation}
\begin{split}
P(\vec{x}) &= P_1(x_1) P_2(x_2) ... P_n(x_n)
\end{split}
\end{equation}
In ΛCDM, H(t0) = 70km/s/Mpc,
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Hi,
In Problem 9.12 of Griffiths Introduction to Electrodynamics, 4th edition (Problem 9.11 3rd edition), in the problem, he says that one can calculate the average energy density and Poynting vector as
using the formula
I don't really understand how to do...
I know I need to measure the density of 7-Up. I can measure its volume, but I don't know how to find its mass.
I also need to determine the composition of sugar in water, and compare 7-Up solution to the known sugar/water mixtures -- I don't know how to do these. Thanks.
When I was reading this page to understand Archimedes' 'story' I got a question:
http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html#buoy
According to the example shown, Archimedes found the density of crown by finding the apparent weight. What if he had just measured the volume of water...
The wave function ψ(x) of a particle confined to 0 ≤ x ≤ L is given by ψ(x) = Ax, ψ(x) = 0 for x < 0 and x > L. When the wave function is normalized, the probability density at coordinate x has the value?
(A) 2x/L^2. (B) 2x^2 / L^2. (C) 2x^2 /L^3. (D) 3x^2 / L^3. (E) 3x^3 / L^3
Ans : D
I have a problem where I am given the density of states for a Fermion gas in terms of momentum: ##D(p)dp##. I need to express it in terms of the energy of the energy levels, ##D(\varepsilon)d\varepsilon##, knowing that the gas is relativistic and thus ##\varepsilon=cp##.
Replacing ##p## by...
Hello All
Typical 'artist's impressions' of the Asteroid Belt show a large density of matter, see the attached view.
Many unmanned spacecraft (and hopefully soon some manned ones) have crossed this belt, without encountering any asteroids, so how close is this view to the truth? Is there any...
I want to begin by writing the problem and drawing its sketch to make things clearer on what is being asked for.
Given : In the sketch shown to the right, the density profile of air with increasing ##z## is given by ##\rho=\rho_0 \exp(-z/z_0)##. Since we know the value of atmospheric pressure...
Hi everyone. Using the Green function, I want to obtain the density of states of a one-dimensional (linear) lattice. Depending on the problem conditions, we will have an iterative loop with 4,000 data for the energy component and a iteration loop with 2,000 data for the wave number component. In...
Using the ideal gas equation ##PV = nRT\Rightarrow PV = \frac{m}{M} RT## where ##m,M## are the mass and molecular weights of the gas respectively.
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If only we can obtain the variation of...
Hi,
I have a question about probability transformations when the transformation function is a many-to-one function over the defined domain.
Question: How do we transform the variables when the transformation function is not a one-to-one function over the domain defined? If we have ## p(x) =...
Hi,
I have question about finding marginal distributions from 2d marginal pdfs that lead to the probabilities being greater than 1.
Question:
If we have the joint probability distribution ## f(x, y) = k \text{ for} |x| \leq 0.5 , |y| \leq 0.5 ## and 0 otherwise. I have tried to define a square...
Hi. For some background, I am running molecular dynamics simulations of silica fracture in LAMMPS. Each point represents the location of a broken bond. I would like to find regions where many bonds are breaking, which I speculate would be locations of crack formation. These computations are...
The current density is given by the formula
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##J_i=n_i(\mu_n + \mu_p)qE## ->eq2
##J_i=60 \text{ ohm-cm} ##
Applying the standard equations...
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In cosmology the deceleration parameter defined as the
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Is there a similar expression for the jerk parameter (##j_0##) ?
this figure form ( https://en.wikipedia.org/wiki/Effective_mass_(spring%E2%80%93mass_system) )
massive spring ; m
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There is a section in the BJT explanation the charge density and the corresponding electric field graphs. But i was not sure how the electric field is derived and hence i started deriving it. Please correct me if my understanding is wrong in posting the question
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As I understand Darcy's law, it computes the flux of water through an area. The same value of flux can be the realized by different combinations of a density of water in the soil and the velocity of that water. So. as far as I can see, Darcy's law is ambiguous about which combination of...
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With ##\rho=\sum_i p_i|\Psi_i\rangle\langle\Psi_i|##If the ##p_i=|\langle\Psi|\lambda_i\rangle|^2## are taken as joint probabilities given by quantum mechanics for the singlet state in EPRB then this cannot represent a statistical mix (classical) of those states because of Bell's theorem ?
1. If today vacuum and matter contribute 71 % and 29 % to the total energy density of the universe, at what redshift z were they contributing equally?
2. If today vacuum, matter, and radiation contribute 71 %, 29 %, and 0.01% to the total energy density of the universe, at what redshift z were...
First of all, I've calculated the partition function:Z=1h3∫e−βH(q,p)d3pd3q=1h3∫e−β(p22m−12mrω2)d3prdrdθdz=2πL(2mπh2β)3/2e12βmω2R2−1ω2mβThe probability of being of one particle in radius $r_0$ is:
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So I've thought that because, by definition, the...
Do we first find out as to what is the gravitational strength of a celestial object and then with that determine its density or do we first know what is its density and then conclude with that as to what is its gravity? Also whether the knowledge about gravitational strength or density comes...
In this explanation we need to involve the Dirac delta functions(maybe) but I clearly have a difficulty in understanding it can some one explain me the whole concept of constant or non constant volume charge density.
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I don't understand the ratio [ 1 g / 6.02*10^23 amu] in the following conversion factor:
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(This calculation is in a problem where you're finding the density of a unit cell in g/cm3 - though it has nothing to do with the...
Hi there, I've worked through most of this question but I'm stuck on the final part, showing that total bulk current ##I_B## is equal and opposite to total surface current ##I_S##. I calculated ##\vec H## the normal way I would if I was looking for ##\vec B## in an infinitely long cylindrical...
Summary:: Given statement: according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is 0.217m^2kg^-1
Given statement: according to one model of the sun, the central mass density is 1.53x10^5kg.m^-3 and the mean opacity at the center is...