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
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.
...
i have a mathematical question which is quite similar to one asked before, still a bit different
https://www.physicsforums.com/threads/derivative-of-first-term-in-lagrangian-density-for-real-k-g-theory.781472/the first term of KG-Lagrangian is: \frac{1}{2}(\partial^{\mu} \phi)(\partial_{\mu}...
< Mentor Note -- Poster has been reminded that they need to use the HH Template and show their work >
A distant alien world has an acceleration due to gravity of g=100 m/s^2. Beings on this planet float in an atmosphere with a density of 5 kg/m^3, and they have a mass of 1 kg. What is their...
Homework Statement
*This is not my whole problem, I am only stuck on how to interpret one part of the question. Put simply, I want to find the expression for the density of energy levels in a given energy band per unit volume (in some crystal structure). Say I have an infinitesimal interval of...
Hey,
I've been searching around online, and I can't find anything on the individual densities of D2 an T3, only the mean density of all hydrogen isotopes.
Thanks,
NWFusor
Homework Statement
I need to find the final impact speed of the flame of a non-uniform candle. I am given that the mass per unit length increases linearly from top to bottom starting with 1kg/m at the bottom and 10kg/m at the top. I need to find how fast the candle flame is moving once the...
Homework Statement
A long, straight wire, radius R, carries total current I. The current is distributed in the wire so that the current
density is proportional to s, the distance from the center of the wire.
(a) Write an expression for the current density J in the wire, as a function of s...
Hi everyone,
I am looking for a way to densify silicone oil. Foolishly, I tried to dissolve Calcium Chloride but as well all know, salt will not dissolve in oil. If anyone has any knowledge as to how I can increase the density of silicone oil I would greatly appreciate your input.
Hey there - I think I have an issue with my 3D density plots of the probability density of the Coulomb wave function. The reason I think something is going wrong is because my plots of |ψ(n=2, l=1, m=-1)|² and |ψ(2, 1, 1)|² are identical, while I would expect them to have the same shape but be...
Hi,
I'm trying to make sense of a wave propagation problem. It's a 1D problem, modelling propagation of density perturbations which travel like waves in a fluid. The problem is governed by the mass and momentum equations and density is related to pressure using the bulk modulus of the fluid...
Hi, may I ask about this:
In a normal orbiting system, if the orbiting object has the right velocity, it will stay in a stable orbit around the more massive one (to be precise, they will both orbit around their common center of mass, but for a galaxy this coincides with the galactic center)...
Hello, I'm a trainee teacher and I'm delivering a lesson with a practical where the students find the densities of various objects. I want to end the class with 8 to 10 true or false questions about density which test misconceptions on density. The one I have is
Is a dense object always heavy...
Homework Statement
There is an electrostatic potential, given by ## \phi(r)=\phi_0 e^{-\alpha r}## where ##\phi_0## and ##\alpha## are some constants.
A: Find the electric charge denisty ##\rho(r)## which produces this aforementioned potential.
A: What is the electric field...
Homework Statement
The problem I have is that we are asked to show the complex relative permittivity of a good conductor is erc = 1 + i(sigma)/(omega*epsilon_0) where sigma is the conductivity and omega is the frequency of an electromagnetic wave in the medium. This is fine, I calculated it...
Homework Statement
A system's state of spin 1/2 is represented at t=0 by C*exp[-a2(p-p0)2]*{{1,0},{0,1}} where the density matrix is represented in the base of eighenvalues of Sz and the spatial vector is represented in the continuum base of statesPx, Py, Pz.
Find <X>, <Px> and <ΔX>, <ΔPx>...
Would the direction of the Magnetic Flux Density vector B at the south side be towards the south pole like this?
and is the direction for B correct for the other side?
One more thing, how can magnetic flux density be a vector and have a direction when its sort of a density, I mean its over an...
Homework Statement
In an atom: suppose one electron orbits the n proton nucleus at radius r . Find the magnetic energy density, in J/m3, at the center of the atom due to the motion of this electron.
NOTE: You can ignore the effect of other electrons in this atom.
Homework Equations...
Homework Statement
A bar suspended in air weighs 1.75 N
The same bar weigs only 1.4 N when suspended in water.
Calculate;
a. upthrust
b. density of the bar
Homework Equations
D = m/v
F = m*a
The Attempt at a Solution
a[/B].
Upthrust is 1.75 N - 1.4 N = 0.35 N
b.
Assuming density of water...
Hi all,
A question about the vacuum energy density and spectrum. The only spectrum that is frame invariant involves the cube of the frequency. Is it also possible to have a constant offset term (which would also be frame invariant), to 'adjust' the energy density so it doesn't turn out to be...
In charge density wave systems in paper http://journals.aps.org/prb/abstract/10.1103/PhysRevB.37.10055
subharmonic steps are detected in experiments from the differential resistance ##\frac{dV}{dI}##, instead of from ##I-V## characteristic. Since the charge density wave resistance is shunted by...
Homework Statement
I am conducting some research and have come across a problem, it could very well be misunderstanding.
I am trying to calculate electron density N.Homework Equations
There was given a simple formula F = 9√N ...
where F = critical frequency and N = electron density...
But...
Homework Statement
The center of a 1.00 km diameter spherical pocket of oil is 1.00 km beneath the Earth's surface. Estimate by what percentage g directly above the pocket of oil would differ from the expected value of g for a uniform Earth? Assume the density of oil is 8.0*10^2 (800) kg/m^3...
Homework Statement
Given a quantum density ρ=w1|φ1><φ1|+w2|φ2><φ2|
where φ1=c(1/2)*exp[-(x-b)2/2c2]
φ2=c(1/2)*exp[-(x+b)2/2c2]
find the density of probability of finding x0 if X(operator) is measured
Homework Equations
PA=Σwi(Σ|<a;α|φi>|2)
The Attempt at a Solution
I know that the probability...
Homework Statement
An 18 carat gold ring is made from an alloy containing 75% gold with small amounts of other metals including copper and silver. By considering the ring to be a cylinder, find an order of magnitude estimate for the mass of the ring.
Homework Equations
density of gold - 19.32g...
Here's the question: http://imgur.com/N60qRmw
I normalized the wave function and got A = sqrt(315/8L^9)
but how would I plot representative snapshots if the exponential factor will cancel when I square it? It's not a mixed state so it shouldn't depend on time as far as I can tell. Should I use...
Here is the problem link picture http://i.imgur.com/0BtcXJk.png
I know that omega=density/critical density
so I know I can find the value of all of those.
DE is dark energy and M is matter (I'm pretty sure).
I assume I have to sub that formula into equation 1, and then rearrange it to create a...
Homework Statement
find μ and σ^2 for the following probability density
f(x) = x for 0<x<1
f(x) = 2-x for 1 <= x < 2
f(x) = 0 elsewhere
Homework Equations
μ = ∫xf(x)dx
σ^2 = ∫x^2 f(x)dx - μ^2
The Attempt at a Solution
first we find the mean. we split up the integral into sums of different...
Homework Statement
If the distribution function of a random variable is given by
F(x) = 1- 1/x^2 for x>1
and
F(x) = 0 for x <= 1
find the probabilities that this random variable will take on a value
a) less than 3
b) between 4 and 5The Attempt at a Solution
since they use the capital F i...
Hello I have question about universe density so is there any equation what says how to calculate universe density because on meany cosmology equations:wink:.
Homework Statement
An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 72 mm. The electric potential of the inner conductor with respect to the outer conductor is -536 V (k = 1/4πε0 = 8.99 × 109 N · m2/C2) The average energy...
Hello to everyone.
My first question on this forum (it was quite tricky thinking of a heading and prefix for this thread!):
Imagine for a moment that there is a hot air balloon which has a strong shell forming the balloons shape rather than one made from material and it weighs the same as a...
Homework Statement
This is a wire whose shape is given by y = acos(x/L). This wire has a linear charge density of +λ, and is it desired to determine the electric field at the point (0,y) where y > a.
a) If a=0, determine the amount of charge the wire has.
b)If a > 0, is the total charge on...
Homework Statement
At what rate would stars have to be producing light (how many photons per second per solar mass start) in order for the energy density of photons in the universe be constant? Assume current values of cosmological parameters. Do it for current time.
Homework Equations
e =...
Homework Statement
If the energy density of the vacuum were the value 10^133 eV/m^3 , what would the value of the Hubble lookback time be for such a universe with no curvature and no other matter?
Homework Equations
Possible equation...
...Lookback time = ln(1+z)/H
The Attempt at a Solution...
Homework Statement
Basically I'm given a feed flowrate - 70,000 gal/day
I know the weight percent is 35% and the component is Triethylene Glycol - density - 1.255g/ml
Homework EquationsThe Attempt at a Solution
So i did this
70,000 gal/day * .35 * (.0378mL/1gal)* 1.255g/mL = g of Triethylene...
Homework Statement
Convert 1 ##Gev## to Kelvin, and convert ##GeV^{-1}## to meters, seconds, and convert ##GeV^4## to density ##(kg/ m^3).##
Homework Equations
natural units ##c=h=k_B=1##
The Attempt at a Solution
I know to convert energy to meters, I can use
##\lambda =hc/E##, I get the...
Homework Statement
a)Find the densities of states 0.08 eV above the conduction band edge and 0.08 eV below the valence band edge for germanium. Be careful with units and be sure to give the units for your answer.
b) Find the volume density of states (i.e. number of states per unit volume)...
I recently bought a 1-pound .999 fine copper bar. I was curious to know how closely the density of my bar was with the actual density of copper (about 8.96 g/cc). My bar measured 1 pound .5 oz (467.76 g). I calculated the volume two ways, water displacement and measurement; the volume is...
Homework Statement
Suppose you take a pass-fail test repeatedly. Let Sk be the event that you are successful in your kth try, and Fk be the event that you fail the test in your kth try. On your first try, you have a 50% chance of passing the test.
P(S1)=1−P(F1)=1/2.
Assume that as you take the...
hi!
i need to solve this integral:
\rho_s=\int (m/\omega)e^{-\omega/T}d{\vec k}
where \omega=\sqrt{m^2+{\vec k}} is the dispersion relation, T is the temperature of the system and m the mass of a particle
Thank you!
If 50kg of salt is mixed with 100 kg of water to form a 1500kg/m^3 solution, can I find the concentration of salt by subtracting the density of water which is 1000kg/m^3, or do I have to equate it like this: 50/((50+100)/1500)=500kg/m^3 ? Is the volume of salt negligible so that the volume of...
Homework Statement
An experiment to measure density, d, of a cylindrical object uses the equation
d=m/(pir^2l)
where
m=mass=0.029 +-.005kg
r=radius=8.2 +-.1mm
l-length=15.4+- .1
What is the absolute uncertainty of the calculated value of the density?
Homework Equations
above
The Attempt...
Homework Statement
a) and b) are no problem.
I need help to solve c) and d)
Homework Equations
c) Delta dirac function
Gauss' law
d) Gauss' law
## \int_V {\rho \, d\tau} = Q_{enclosed} ##
The Attempt at a Solution
By taking laplace on the potential I get:
## \rho(\mathbf{r}) =...
Homework Statement
a) A material is composed of two atoms, A with effecitve radius 2.00 angstroms and B with effective radius 3.10 angstroms. The lattice is a body-centred lattice.
b)Enter the volume density of either the A or B atoms in atoms/cm3
Homework Equations
.5*sqrt3=(r1+r2)
surface...