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
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...
Hi,
I was recently thinking about a problem which I have no idea how to solve.
A full water container with volume V is hanged on a rope with length L (mass of the rope is negligible). It then starts to revolute around the point where the rope is hooked (circular motion, circle with radius L)...
Homework Statement
I need to find three potential reasons for my .5% error in a lab where I used the Archimedes Principle to measure the density of Iron. We only used a graduated cylinder full of water and an iron mass. I measured the water level from the meniscus. We used two different...
Homework Statement
Homework Equations and attempt at solution
I think I got the ground state, which can be expressed as |\Psi \rangle = \prod_{k}^{N}\hat{a}_{k}^{\dagger} |0 \rangle .
Then for the density matrix I used:
\langle...
Derive the probability current density for a particle
in an electromagnetic field.
(I previously posted this on StackExchange. Please pardon,
but I have been spending a lot of time on this and if anyone
knows exactly what the subtle trick involved is, I
would really appreciate it.)...
I have data which gives me the magnitude density (mag arcsec-2) of M31 as a function of radius. How can I convert this data to the (enclosed) mass at a given radius (for Velocity Curve analysis)?
Homework Statement
We know that after long run of simple mass-spring system, there should be a probability of finding the mass at certain points between -A and A.. Obviously in probability of finding the particle near A or -A is higher than finding the particle at 0, because the speed is the...
Hi... any idea on how to calculate force needed to pull up something stuck on the ground?
ex:
Boot stuck on mud
person sinking on quicksand
or car sinking in water
G’day physics forum
This is a purely hypothetical question and my knowledge of physics is rather limited so I’ve no idea if answering it is even possible however here goes:
Imagine a 30cm long timber stick approximately 3mm in diameter that has been placed vertically in an inverted pyramid or...
Hi!
I am a freshman in college on my first week of an intro chemistry course. I think the professor may have made a mistake with the software that generates the problem sets, but I'm giving it a shot regardless.
One of the questions is: An alloy with a 1:1 ratio of magnesium and strontium...
This is a bit of a random project I am looking into. Recently a product was released called the beer bug. It measures the density of beer by tracking the weight of a submerged buoy. They calculate change in density based on changed in weight and then calculate % alcohol (ABV) from that...
Homework Statement
A rather large non conducting slab of area A and thickness d has a charge density given by ρ = αx2.
The origin is through the center of the slab. That is, it bisects the slab into two equal volumes of d/2 thickness and with an area A, with -L/2 to the left of x=0 and L/2 to...
Homework Statement
"Calcium crystallizes in a body-centered cubic structure. (a) How many Ca atoms are contained in each unit cell? (b) How many nearest neighbors does each Ca atom possess? (c) Estimate the length of the unit cell edge, a, from the atomic radius of calcium (1.97A). (d) Estimate...
Homework Statement
Perform potential energy W of a non-uniform density sphere by density d=d(r) and o(r)=dW/dm.
Homework Equations
The answer is W=1/2.integral(from 0 to R)(4x3.14xd(r)xo(r)xr^2xdr).
The Attempt at a Solution
I have solved this by this way:
o(r)=-GM(r)/r...
Homework Statement
Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and...
This is a diagram of a pitot-static tube. My question is however not related to its applications but rather, what causes the liquid to rise up the static tube? The static tube is at right angles to the fluid flow. I understand that this is a very basic question but I can't seem to get my head...
Homework Statement
Show that the density of water at a depth z in the ocean is related to the surface density rho_s by
\rho(z) \approx \rho_s [1 + (\rho_s g/B)z]
where B is the bulk modulus of water.
Homework Equations
B = -V (dP/dV)
B = rho (dP/d rho)
3. The Attempt at a Solution
I've...
At a temperature of 0 C the density of ice and liquid water is 0.9187 g/cm3 and 0.9998g/cm3 respectively. Consider a situation where the density of ice is increased to more than 8.83% at 0 C, what would be the consequences of this to the life forms?
The life forms would vanish because of the...
Homework Statement
So I saw a unit "W/(g2 cm3)"
And I'm pretty sure it's about power density...and I understand what W/cm3 is. It's watts per cubic centimeter...but what does the g mean? grams? If so, how does that fit in? :/[/B]
Hi.
Bell's formulation of local realism is $$P(a,b)=\int\ d\lambda\cdot\rho(\lambda)p_A(a,\lambda)p_B(b,\lambda)\enspace.$$
Let's for simplicity assume there's only a finite number of states, so this becomes $$P(a,b)=\sum_{i} p_i\cdot\ p_A(a,i)p_B(b,i)\enspace.$$
I'm trying to translate this...
Hey All,
I was wondering if anyone knows of any good simulation software packages that can do quantitative radiometry. I'm thinking COMSOL may have a radiometry suite, but I'm not very familiar with the software or package offerings.
Basically, I'm trying to optimize the placement of hundreds...
Homework Statement
You've probably noticed that TV screens and computer monitors have an annoying tendency to accumulate dust. Wanting to understand this better, you decide to model the situation as follows: you assume a small mote of dust might have an excess charge of 1 nC and a mass of 5...
Suppose we have an elliptical loop of wire in the x-y plane with constant cross-section. And let's also assume that the cross-section is very small, so we have a thin wire.
$$\vec{r}=\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} a\cos \theta \\ b \sin \theta \end{bmatrix}$$
A tangent...
Hi, I'm trying to write the current density for such circular loop in spherical coordinates. For a circular loop of radius a that lies in the XY plane at the origin, the current density it's simply:
\mathbf{J}= \frac{I}{2\pi\sin\theta}\delta(\theta-\frac{\pi}{2})\frac{\delta(r-a)}{a}\hat{\phi}...
Dear friends,
Does anyone know how we can solve the TOV equations for a non constant density?
In all the references, I just saw the solution for a constant density.
Thanks in advance for the help :)
I'm sorry for my bad English.
Let X a completely Hausdorff space. Will the be space of all continuous real-valued functions on a space X with the topology of pointwise convergence dense in the Tychonoff product ℝX?
I am doing research and I need to find the dark matter density of Galaxies or dust clusters (It can be any type of thing) which the distance from Earth will be ≅4000 Mpc.Here the picture
Think the radius of sphere.
Dear Friends!
Probably more than a decade back understanding tells us : If the average matter density of the universe happens to be smaller than a critical value,then the galaxies will never come to a halt and turn back(Open Universe).Which will imply cold and lonely death.
If on the...
I've never been able to figure this out. I can understand when you put oil in water that one floats on top of the other, but why does it still work if I put it into a balloon? Something that keeps it from directly interacting with the medium it's in?
Everything as follows:
I'm looking to calculate the amount of NaCl (rho=2.19 g/cm^3) needed to add to water (rho=0.999 g/cm^3) to achieve a solution with density=1.071 g/cm^3. Ideally, I want to achieve an Atwood Number of 0.035 and a density of 1.071 g/cm^3 is what I need for the solution...
Okay, so this is the website: <Moderator's note: link deleted as it is not a valid reference>
I found this page as I was looking for a way to compare the assumed gravitational constant of the moon and the acceleration of the hammer/feather from the Apollo 15 experiment video. I have only taken...
Homework Statement
Find the total charge Q given the charge density ρ(r)=ε0A(4πδ3(r)-π2e-λr/r
The Attempt at a Solution
I know the solution's steps start with: Q=∫ρdr=ε0A(4π∫δ3(r)dr-λ2∫e-λr(4πr2)/rdr)
What I don't understand is where that 4πr at the end comes from. That last step is only...
Homework Statement
This isn't really a problem I've been given, but questions i have about how the author of my textbook, Leon Couch, Digital and Analog communications Systems, found the PSD (power spectral density) of an digital NRZ pulse train.
Homework Equations
The PSD of a periodic signal...
Hello all, I have been arguing about this for a few days. My friend is telling me that a helicopter flies in the air because there is a difference in density on top of the propeller and below the propeller.The air on top of the helicopter has less density and the bottom has more density. This...
Hello everyone,
I have a physics problem that I have been struggling with for a long time. Many many hours of searching around for theoretical or practical answers have not given me anything definitive.
The question is in the context of electrical engineering, more specifically peaks in...
I was watching a lecture in which the professor derived the Navier Stokes Equations for const density and viscosity. He however skipped a step and directly went from one equation to another without giving any explanation. I have attached an image file in which the 2nd equation is derived from...
Hello all,
Is there any direct relation ship exists between the thermal expansion and density of polymer material (eg. PMMA, Teflon) ?
Like, Lorentz- lorentz law relates directly the refractive index and density of the polymer.
similarly any laws relating (thermal expansion and density of...
Electromagnetic field has a density of energy
U = ε/2*E2+ μ/2* H2
And a density of momentum, given by the Poynting vector
S = E x H
For an element of volume dV you have a four vector of energy and momentum which is
[E,P] = dV * [U, S]
Being E the energy in the element of volume and P the...
Hope I'm in the right section for this question! In the big bang model, the expansion of the universe is slowed down by gravity. If there is enough matter in the universe, then the expansion can be overcome and the universe will collapse in the future. The density of matter that is just...
Homework Statement
Calculate the surface density (planar density) of the Silicon diamond structure in the [1 0 0],[1 1 0],[1 1 1] planes.
Given a = 5.431 A (latice constant)
Hint: For the (111) plane, it should help you to think of the diamond lattice as two interpenetrating FCC lattices.2...
In wikipedia says Physical baryon density: ##Ω_bh^2=0.02230±0.00014## and
Physical dark matter density:##Ω_ch^2=0.1188±0.0010##
Matter density:##Ω_m=0.3089±0.0062##
so If we collect baryonic matter density and dark matter density we...
Homework Statement
Sakurai Modern Quantum Mechanics Revised Edition. Page 81. density matrix p = 3/4 [1 0; 0 0] + 1/4 [1/2 1/2; 1/2 1/2]. We leave it as an exercise to the reader the task of showing this ensemble can be decomposed in ways other than 3.4.24Homework Equations 3.4.24 w( sz +...
A disk with a uniform positive surface charge density lies in the x-y plane, centered on the origin. The disk contains 2.5 x 10-6 C/m2 of charge, and is 7.5 cm in radius. What is the electric field at z = 15 cm?
I have used the formula...
There are two numericals,
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In other numerical
2. Concentration of H2SO4 is 98% by mass having density of 1.84gm/ml. Calculate Molarity.
here they used another formula.
now my...
Normal density of Earth is 5,5 tons/m3 and surface gravity is 9,8 m/s and. But if we would compress mass of Earth to 50 km diameter, we would get density 1,4 mil tons/m3 and surface gravity would be 158 860 m/s.
I know the math, in basic gravity equotation F=Gm1m2/r2 with decreasing r you get...
Hi... I want to know why charge density is higher at sharp points in a conductor? I have gone through the analogy of two spheres connected by a wire... But is there any other explanation which is not specific to spheres...?
Homework Statement
Random variable X is uniformly distributed on interval [0,1]:
f(x)=\begin{cases} 1 & \text{ if } 0\leq x\leq 1\\ 0 & \text{ else} \end{cases}
a) Find probability density function ρ(y) of random variable Y=\sqrt{X} +1
I tried like this. Is it good, if no why not...
Hello.
I'm studying principle of Langmuir probe and got several questions.
1st, the textbook suddenly tells that ion density within sheath is
ni(x) = nis(Vs/V(x))1/2
where nis, Vs are ion density and plasma potential at sheath edge.
I found some document which shows that it is obtained by...
Homework Statement
The figure shows a composite slab with dimensions d1 = 11.6 cm, d2 = 2.85 cm, and d3 = 13.4 cm. Half the slab consists of aluminum (density = 2.70 g/cm3) and half consists of iron (density = 7.85 g/cm3). What are (a) the x coordinate, (b) the y coordinate, and(c) the z...