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.
I'm reading this paper. But I haven't read anything on how to calculate the density operator in a QFT or how to calculate its trace. Now I can't follow this part of the paper. Can anyone clarify?
Thanks
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Consider an ensemble of spin 1 systems (a mixed state made of the spin 1 system). The density matrix is now a 3x3 matrix. How many independent parameters are needed to characterize the density matrix? What must we know in addition to Sx, Sy and Sz to characterize the mixed...
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Volume charge density in some space is given by a function ##ρ_v(x)=-ρ_0\frac{x}{a}e^{\frac{-x^2}{a^2}}## where ##ρ_0, a## are positive constants. Determine the electric field vector in arbitrarily chosen point in space.
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3. The Attempt at a Solution...
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Calculate the electric energy density at the surface of a 3.4 mm diameter copper wire carrying a 28 A current.
Homework Equations
u = (1/2) ε0 E2
The Attempt at a Solution
With the electric energy density equation, I substituted in the equation for the electric field for an...
Homework Statement
Calculate the single-particle density of states ##g(\epsilon)## for the dispersion relation ##\epsilon(k) = ak^{\frac{3}{2}}## in 3D. Use ##g(k) = \frac{Vk^2}{2\pi^2}##.
Homework EquationsThe Attempt at a Solution
This question is worth lots of marks. My solution is a few...
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A long rope with mass m = 10 kg is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope and the pulse travels up the rope.
(a) Explain why the speed of the wave pulse change as it moves up the rope; does it increase or...
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An oscillator is attached to one end of a horizontal string. The other end passes over a frictionless pulley and is held taught by a mass m. The distance between the oscillator and the pulley is 1.2m. The string has a linear mass density of 1.6g/m and the frequency of the...
1. Homework Statement :
Homework Equations :[/B] A conductor is an equipotential surface. The charge density near a conductor is proportional to the electric field. Electric field is the negative gradient of potential and thus electric field is in a direction normal to the surface.The Attempt...
Hi,
If you had a sealed round bottomed flask on some lab scales and you recorded the mass and then you removed all the air with a vacuum pump and then found the mass of the flask again would the difference between the two readings really be an estimate of the mass of the gas in the flask? The...
This thing has been bugging me lately that can the constant mass density phenomenon of the universe may not be due to inflation? Can it be considered a consequence of the Casimir effect on the ( Supposed) boundaries of the universe?
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Hello :) This is a last resort. I'm stuck on what to do to complete this lab report table.
We are required to conduct an online simulation at this link: Buoyancy Online Simulation
This is the document of the lab report I'm required to fill up (I'm stuck at part 2)
Homework...
I'm trying to plot the density parameters against redshift in Python, so I suppose this is kind of a cross over of programming and physics. I've been given the following two equations in order to do so
$$r(z) = \lambda_H \int_{0}^{z} \frac{dz'}{E(z')}$$
$$E(z) = \frac{H(z)}{H_0} = \sqrt...
Stage II and stage IV can be used to determine as the volume of the water displaced is given.
Now how should the density be calculated :D
I know the formula for density
$density=\frac{mass}{volume}$
Homework Statement
Find the center of mass of an inverted cone of height 1.5 m, if the cone's density at the point (x, y) is ρ(y)=y2 kg/m.
Homework Equations
The formula given for this problem is rcm=1/M * ∫rdm, where M is total mass, r is position, and m is mass.
The Attempt at a Solution...
The formula for the radiation pressure P in n-dimensional space for a given internal energy density u is ##\frac{u}{n}##.
I would really appreciate it if someone could provide a link that gives a simple derivation of this formula for dummies like me.
Question:
On the Moon, the force of gravity on an object is only about one-sixth of its value on Earth. Decide whether each of the following would give an accurate measurement of the mass if used on the Moon
a) A beam balance like the one in the diagram at the top of the page
b) A balance...
I was overlooking page 47 of "The Physics of the Manhattan Project" 2.2 Critical Mass: Diffusion Theory, and author Bruce Cameron Reed reported that:
Can anyone explain how Bruce Cameron Reed got from (2.18) to (2.19)
I tried plugging ## N(r,t) = N(r) N(t) ## into (2.18) to get (2.19), but it...
Homework Statement :
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The density of the Earth's atmosphere varies with altitude, and can be approximated by an exponential: ρ(h)=ρ0e^(-h/h0) where ρ0 = 1.3 kg/m3 (the approximate density at sea level) and h0 = 8.2 km (this is determined empirically). Calculate the mass of 15 km of the...
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The magnetic flux density in the vicinity of a large air-cored electromagnet is determined by measuring the induced flow of charge in a small coil as the current in the electromagnet is switched on -- see the diagram below.
Calculate the magnetic flux density at the...
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Two long, coaxial metal cylinders are separated by a material of conductivity sigma and dielectric constant epsilon. The radius of the inner cylinder is a, the radius of outer cylinder is b, and the length of both is L.
Suppose that the inner conductor is held at a...
I'm trying to learn some basic quantum mechanics, mostly from I a mathematical perspective. I am trying to understand this with quantum states as vectors in a Hilbert space, bipartite systems, the difference between superpositions and ensembles of states, and density matrices. And it is the two...
In Jackson, the following equations for the vector potential, magnetostatic force and torque are derived##\mathbf{m} = \frac{1}{{2}} \int \mathbf{x}' \times \mathbf{J}(\mathbf{x}') d^3 x'##
##\mathbf{A} = \frac{\mu_0}{4\pi} \frac{\mathbf{m} \times \mathbf{x}}{\left\lvert {\mathbf{x}}...
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In the picture below it is asked that i calculate the resultant electric field if the linear charge density is known.
Calculate the resultant electric field of a charged semicircle wire (positioned as in the picture) at some point M on the Z axis if the linear charge density...
Homework Statement
Two identical wires R and S lie parallel in a horizontal plane, their axes being 0.10 m apart. A current of 10 A flows in R in the opposite direction to a current of 30 A in S. Neglecting the effect of the Earth's magnetic flux density calculate the magnitude and state the...
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An electromagnetic wave propagates through a gas of N free electrons per unit volume. Neglecting damping, show that the index of refraction is given by
n^2 = 1 - \frac{\omega_P^2}{\omega^2},
where the plasma frequency
\omega_P = \sqrt{\frac{Ne^2}{\epsilon_0m_e}}.\quad(1)...
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A long air-cored solenoid has two windings wound on top of each other. Each has N turns per metre and resistance R. Deduce expressions for the flux density at the centre of the selenoid when the windings are connected (a) in series, and (b) in parallel, to a battery of EMF E...
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The electric dipole moment for the water molecule equals $$ p = 6.13 × 10−30 C · m $$ Suppose that in the glass of water all molecular dipoles could be made to point down. Calculate the resulting surface charge density at the upper water surfaceHomework Equations
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## P...
Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate...
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Hi everybody! I'm preparing for an exam of electromagnetism, and I am struggling with the last question of this problem (hopefully the two first ones are correctly solved):
Given potential: ##\phi(\vec{r}) = k \frac{q}{r} e^{-r/R}## with ##r=\sqrt{x^2 + y^2 + z^2}## and ##R...
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A long wire (X) carrying a current of 30 A is placed parallel to, and 3.0 cm away from, a similar wire (Y) carrying a current of 6.0 A. What is the flux density midway between the wires: (a) when the currents are in the same direction, (b) when they are in opposite...
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A function, ##f\left(x\right)=\left|a^{\frac{\sin \left(x\right)}{\ln \left(ax\right)}}-\frac{x}{a}\right|##, intersects with another function, ##g\left(x\right)=\left|\frac{sin(ln(\sqrt{x}-\sqrt{a}))}{x^2-a^2}\right|##, at point ##Q(b,f(b))## and point ##R(c,f(c))##. A...
I thought that insulators cannot be charged in the inside or the outside, so how can they have any charge density inside? I know that electric fields pass through a insulator, so is that why they can have charge density? I am currently reading about electric flux.
Consider two atoms of platinum, A and B, in a sample of platinum. Atom A lives deep within the sample, and atom B lives at the tip of a sharp protuberance at the surface. My understanding is that electrons in the sample will accumulate within a surface defect such as the tip of a sharp needle...
At this point I was given rho, sigma and landa to hold value of these three different kinds of density
ρ = Charge/Volume -------------- Volume Density
σ = Charge/Area ----------------- Area Density
λ = Charge/Length ---------------- Length Density
How do I know which type of density to use over...
I read that niobium metal has a Cooper-pair density of about 10^22 per cubic centimeter. However, when a current flows through a superconductor my understanding is that it all flows near the surface, beginning at the London penetration depth, which is a very small distance.
So, let's say that...
So my question is, is there a relationship between the density of a medium you are traveling through and the maximum speed achieved for an object of constant mass and shape traveling with constant thrust in both mediums?
for example if i knew that an object traveled 8 times faster in 1 medium...
1) If I vary charge densities, but keep current density constant, do I get any sort of electromagnetic wave?
2) If the answer to question 1 is no, then if I vary charge densities, but keep current density constant, could I conceivably have a two isolated "open circuit" current elements of...
I'm starting out on DFT right now.
I'm an experimental Physics student, so I'm not very familiar with theories.
Can you recommend any good textbooks or resources that I can utilize for my study??
Thanks in advance.
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This is a basic cosmology problem.
The Friedmann equations are
##\Big( \frac{\dot{a}}{a}\Big)^{2}+\frac{k}{a^{2}}=\frac{8\pi}{3m_{Pl}^{2}}\rho## and ##\Big( \frac{\ddot{a}}{a} \Big) = - \frac{4\pi}{3m_{Pl}^{2}}(\rho + 3p)##.
Using the density parameter ##\Omega \equiv...
Hi,
In an article on theoretical fluid dynamics I recently came across the following equation:
$$M_i = \sqrt{g} \rho v_i$$
where ##M_i## denotes momentum density, ##v_i## velocity, ##\rho## the mass density and g is the determinant of the metric tensor. It is probably quite obvious, but I do...
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As I understand it, the Universe is red-shifted (emission spectra) from any point of reference looking outwards. The Universe is expanding, but is matter being created at the same rate ? Does this mean that the density of matter in space is decreasing ? (density = mass / volume). What does this...
Hello Forum,
I am revisiting Archimedes principle and its important consequences.
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Homework Statement
Given a density matrix of three qubit pure state, how can I know after do some transformation, this state belong to what class?. Class I mean here, either separable state, biseparable, GHZ state or W state?
I mean here what is the indicator to me classify it?
It is the...
When one reduces the intensity of let's say, an incandescent bulb (by varying the resistance, as seen in many homes), which decreases more, the photon frequency (not related to wavelength, but the time interval between photon emissions) or the areal density of the photons?
To what extent does...
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A hollow sphere of inner radius 9.0 cm and outer radius 10.0 cm floats half submerged in a liquid of specific gravity 0.80. (a) Calculate the density of the material of which the sphere is made.
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A block hangs by a cord from a spring balance and is submerged in a liquid contained in a beaker. The beaker in turn rests on a kitchen scales. The mass of the beaker is 1 kg, the mass of the liquid is 1.5 kg. The spring balance read 2.5 kg and the kitchen scales reads 7.5...