What is Energy density: Definition and 201 Discussions

In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It may also be used for energy per unit mass, though a more accurate term for this is specific energy (or gravimetric energy density).
Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored. In cosmological and other general relativistic contexts, however, the energy densities considered are those that correspond to the elements of the stress–energy tensor and therefore do include mass energy as well as energy densities associated with the pressures described in the next paragraph.
Energy per unit volume has the same physical units as pressure, and in many circumstances is a synonym: for example, the energy density of a magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a compressed gas a little more may be determined by multiplying the difference between the gas pressure and the external pressure by the change in volume. A pressure gradient has the potential to perform work on the surroundings by converting internal energy to work until equilibrium is reached.

View More On Wikipedia.org
Recent contents Top users
  1. e2m2a

    Question about energy density in On the Electrodynamics of Moving Bodies

    In section 8 of Einstein's On the Electrodynamics of Moving Bodies Einstein uses the expression A(sq)/8 pi. He states this represents the energy of light per unit volume. Does anyone know how he derived this?
  2. I

    Energy density of photons and matter

    hi im doing a question at the moment and am having issues understanding the question, and i can't ask my lecturer as he is stuck abroad with no internet. the question asks to calculate the ratio of current energy density of CMBR photons to that of baryonic matter. the present density of...
  3. WCOLtd

    Does Energy Density Affect Gravitational Field Strength?

    This might sound like a dumb question but I wanted to know if energy density has an effect on the gravitational field, for instance say there are two masses of equal density, one say is a low temperature neutron star and another is a white dwarf (please exclude for now any impossibilities...
  4. F

    Why is the electric energy density in classical electromagnetism underspecified?

    http://farside.ph.utexas.edu/teaching/em/lectures/node56.html By equation 595, electric energy in the universe caused by an electric field is derived as http://farside.ph.utexas.edu/teaching/em/lectures/img1261.png. However, how come you can differentiate with respect to volume and say that...
  5. Z

    Calculate Redshift Where Radiation and Matter Energy Densities Equal

    Hello. This is question for my course work, I was wondering if I could get some insight, here is the question: Assume that the vast majority of the photons in the present Universe are cosmic microwave radiation photons that are a relic of the big bang. For simplicity, also assume that all the...
  6. C

    Energy Density with Thomson scattering

    Homework Statement If ne represents the electron density and the interaction between particles is the photons scattering off of the electrons through the Thomson cross section, how low must the electron density be to cross the universe with no scattering? Homework Equations The size...
  7. J

    Applying amperes law and faradays law to a solenoid and energy density

    This isn't really a homework problem, I just need to know how to do a problem similar to this one for the final and I don't want to fail, so I posted it here. A solenoid with n turns per unit length, length l and radius a (l>>a) has a current I(t)==Io sin(wt) [w is omega], where I and w are...
  8. G

    Understanding Energy Density and Kinetic Energy Spectrum

    and what is kinetic energy spectrum?
  9. R

    Energy density of grav. field - analagous to EM

    The electromagnetic energy density is well-defined through the square of the Maxwell Field tensor. Why cannot such a quantity be defined for the grav. field?
  10. S

    Energy density expression of a Gaussian pulse

    Hi, Energy density of the ith annular section of a Gaussian pulse is written as F(r_i, r_i+1)=2*totalEnergy/[(r_i+1^2-r_i^2)*w^2]*integral(r*exp(-r^2/w^2),from r_i to r_i+1) where r spans from r=0 to r=r_n (theoretically infinity) in n steps, w is the waist size of the beam. This...
  11. G

    Energy Density of the gravitational field

    Why is there no satisfactory way to define the energy density of a gravitational field? Why must we use global energy concepts? I'm currently reading proofs of the Positive Energy Theorem, but none of the references explains why this is so. Can anyone explain it or point me to a good reference?
  12. F

    Info regarding energy density of empty space?

    Hi, new guy here. I once saw a graph on the development of the energy density of the universe, with the X axis measuring time (I believe it was in billion years or so) while the Y axis meansuring the density. There were three lines in that graph, energy density of empty space, energy...
  13. nicksauce

    Energy density of massive neutrinos

    Does anyone have an up-to-date reference for the best value of \Omega_{\nu}, given our current understanding of neutrino masses? Dodelson's cosmology book has \Omega_{\nu}\approx 10^{-3}, but something more recent would be nice.
  14. B

    Understanding Energy Density and Cosmic Expansion

    I know the concept of the accelerating universe and expansion and all, but what exactly is energy density and how does it cause or explain the cosmic expansion of our universe? Thanks in advance.
  15. K

    What is the proposed solution to the Vacuum Energy Density Crisis?

    I have done some research that has led to a possible soultion to the 120 orders-of-magnitude VED disparity betwen the VED of particle physics and the VED measured by cosmology. Nobel Prize-winner F. Wilczek calls the VED crisis a horrendous problem, indicating that there is something...
  16. F

    Temperature Change in a Radiating Sphere with Increasing Radius

    Homework Statement The density of the energy of radiation in a cavity at temperature T is u(T) = aT^4. Suppose the cavity is a sphere whose radius increases at a rate of: \frac{dr}{dt} = v_0 Assuming that no energy enters or leaves the enclosure, will the temperature increase or decrease...
  17. N

    Exploring Energy Density: A Homogenous Unit Analysis

    hey guys this is my first post to the forum so excuse me if I am posting at the wrong topic :D My question is the following: " Energy density is the energy stored per unit volume. Show that the expression of energy density is 1/2 Strees X Strain in homogenous with respect to units "...
  18. A

    Why Is the Left Term of Equation 539 Eliminated in Electrostatic Calculations?

    The original web http://farside.ph.utexas.edu/teaching/em/lectures/node56.html Reading the web which is posted above I got a question ... I need some masters to help me! My question : why not to remain the left term of eq539 instead of eliminating it by "Let us...
  19. G

    Cosmology, K=0, Matter dominated, energy density

    Homework Statement For K=0 of matter dominated universe, i.e at z>>1, find the energy density of starlight if f portion of matter condensed in solar type stars and the stars are uniformly distributed in space. Homework Equations Friedman eqn: \rho_m = \frac{3H^2}{8 \pi G} The...
  20. U

    Energy Density in the Electric Field of a Charged Sphere

    Homework Statement A charged isolated metal sphere of diameter 10cm has a potential of 8000V relative to V=0 at infinity. Calculate the energy density in the electric field near the surface of the sphere Homework Equations u=1/2[tex]\(epsilon x E^2) E=kq/r^2 The Attempt at a...
  21. M

    Energy Density & Pressure

    Part-1:Mass In the context of cosmology, the Friedmann-Acceleration equation highlights the need to understand the components that contribute to both the energy density [\rho] and pressure [P]: [1] \left(\frac {\ddot a}{a} \right) = - \frac {4 \pi G}{3} \left( \rho + \frac {3P}{c^2} \right)...
  22. S

    Capacitor with radius finding the energy density

    A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm , and the outer sphere has radius 16.5 cm . A potential difference of 100 V is applied to the capacitor. What is the energy density at r = 12.6 cm , just outside...
  23. C

    Energy density of electric field

    Homework Statement Assume that 10% of the energy dissipated by a 40W light bulb is radiated isotropically in the form of light. What is the magnitude of he E-field at a distance of 1m? What is it for sun light on the Earth's surface, given the Sun provides ~ 1400W/m2>Homework Equations Energy...
  24. H

    Entropy and Energy Density from a Partition Function

    Homework Statement Partition Function: Z = 1/N! [8 pi V (kT/hc)^3]^N There are several parts to this but here are the parts I'm struggling with: a) Compute the entropy of the system S. b) Computer the energy density u and compare the result with the corresponding results for a...
  25. F

    Deriving Electric Field Energy Density: A Guide

    Homework Statement I found on Wikipedia the formula for energy density of an electric field in a vacuum to be U = \frac{1}{2}\epsilon_0 E^2. I was wondering if someone could point me in the right direction to figure out how this was derived. Homework Equations The Attempt at...
  26. T

    What is the energy density of sunlight on Earth and near the surface of the sun?

    [SOLVED] Energy Density of Sunlight Homework Statement Use the solar constant (1350 W/m^2) to calculate the energy density of sunlight at a)Earth and b) near the surface of the sun. Homework Equations Stefan-Boltzman = (2pi^5)/(15(h^3)(c^2)) h=6.63x10^-34 j.s L(solar...
  27. X

    Energy Density of a Charged Sphere?

    Homework Statement Since this was on the test, I won't be able to type out the question verbatim, but here it goes: You have a plastic sphere with charge equally distributed through out the sphere. The radius of the sphere is a. The energy stored in the total sphere is E0 (not to be...
  28. M

    Deriving Electric Field Energy Density for Arbitrary Charge Distribution?

    Homework Statement Provide a proof for the electric field energy density of an arbitrary charge distribution using basic notions of electrostatics. Homework Equations The energy density for an electric field is w = \frac{1}{2} \epsilon E^2 The Attempt at a Solution I am not sure at...
  29. S

    Converting mks energy density to cgs

    Homework Statement In the SI system, the energy density of the electric and magnetic fields is: u = \frac {\epsilon_{0} E^{2}}{2} + \frac{B^{2}}{2 \mu_{0}} From the equation above, derive an exact expression for the energy density U in the Gaussian system of units. The...
  30. marcus

    What energy density expected at LHC point of collision?

    I'm more used to seeing colliders rated by the kinetic energy of the colliding particles, but just recently I've been seeing estimates of the ENERGY DENSITY to be expected right at the point of collision. This raises doubts about exactly what is meant. what is the nominal area of collision...
  31. Y

    Calculating the redshift at which radiation energy density equaled mass density

    how do you calculate the redshift at which the universe shifted from radiation dominated to mass dominated i was told to assume a flat universe with H0 = 70 also the temperature, to which i was given the formula density rad = aT^4 for the first part, i tried using density is propotional...
  32. S

    Electric Field Energy Density 3-Form Explained

    Here's is a quote from Electromagnetics by Richard H. Selfridge, David V. Arnold, and Karl F. Warnick: I am still not sure where that 1/2 factor comes from...
  33. S

    Finding Electric Energy Density

    Homework Statement Find the electric-field energy density at a point which is a distance of 10.0 cm from an isolated point charge of magnitude 7.30 nC. Homework Equations u = \frac {1} {2} * e_{o} * E^{2} The Attempt at a Solution u = \frac {1} {2} * 8.85*10^{-12} * 7.30^{2}...
  34. R

    Gas pressure v. energy density

    What is the relationship between pressure and the energy density? I note that the units for pressure (force/area) are the same as (energy/vol) but I am curious to know why this is. Thanks.
  35. L

    Vacuum Energy Density & Mass: 4th Power Relation

    Homework Statement Show that, in natural units h=c=1, an energy density may be expressed as the fourth power of a mass. If the vacuum energy contributed by a cosmological constant is now of order of the critical density, what is the mass to which this density corresponds? 2. The attempt...
  36. C

    Energy Density vs Total Energy

    Here is a detail that makes me doubt: Homework Statement I am given the equation for a standing wave with a dependence in 't' and 'z' only... I am told that the wave is propagating in a confined space (2*2*2) m Q1. Calculate the energy density for n=1,2,3. I didn't have any pb with this...
  37. B

    Understanding Pointlike & Local Energy Density

    How do you name a physical quantity that can be defined at a given point in space: pointlike? local? Say energy density.
  38. T

    Differentiating Black Body Energy Density: Seeking Answers

    Hi all, I hope everyone is well and that life is treating you all good. I am going to be honest with my question and say that I have not tried to do it myself yet. I, unfortunately, do not have time now to try and then repost so I do hope you will all forgive me for just stating a...
  39. S

    Scalar field pressure and energy density

    Hi all, I'm hoping someone can help me out as I'm really stuck. With reference to the top of page 7 at http://faculty.washington.edu/mrdepies/Survey_of_Dark_Energy2.pdf I'd like to know how to get the quoted energy density and pressure of phi from the stress-energy tensor. I am very...
  40. T

    Integrating EM Energy Density: Is E=hf?

    when you integrate the energy density (from electromagnetic field) times the differiential volume of the whole 3D space for a photon...would you get the energy of it? E=hf ? one more question... if there is a positive charge in 3d space... when i integrate the electromagnetic energy density...
  41. P

    Transverse Wave Incident on Absorbing Surface: Pressure & Energy Density

    Suppose a light wave is traveling in the z-direction. Then the Electric field is in the x direction, and the B field is in the y direction. My understanding is that these E and B fields are independent of the x and y directions, respectively. This is to say, that if I take the partial...
  42. A

    Calculating Energy Density of a Sphere: Uncovering the Extra 3 in the Equation

    Let's say that the electric field near the surface of a sphere or radius R is E. I need to show that the energy density D is D=\frac{\epsilon_{0}e^{2}}{2}. I started by noting that U=\frac{1}{2}Q\Delta V=\frac{kQ^{2}}{2R}. The volume of the sphere is \frac{4}{3}\pi R^{3}. This is how I...
  43. E

    Relating Radiancy to Energy Density?

    I'm looking through some of my physics notes where we derived radiancy equations for black body radiation (Rayleigh-Jeans and Planck), and I have a quick question. In class, we went through the derivation for the energy density as a function of frequency and temperature. However, I can't find...
  44. marcus

    Who here has calculated the dark energy density?

    It is good practice to calculate the dark energy density. I remember doing it a few years back and later posting the result here at PF. As I recall it was about 0.6 joule per cubic kilometer----so if you were being not overly finicky and giving a rough approx, it was about HALF a joule per...
  45. R

    Qm probability, energy density and curvature

    In qm the intensity (energy density) of an EM wave is compared to the probability of finding a particle at a certain position in space at a certain time.For a particle that isn't moving, according to general relativity, Too = energy density and energy density gives curvature of space time...
  46. marcus

    What was the Maximum Energy Density at the Onset of the Big Bang Expansion?

    the big bang has been studied by a number of people and found not to contain a singularity (the density does not go infinite but has a finite limit) a good recent paper is http://arxiv.org/gr-qc/0407074 Genericity of the Big Bounce in isotropic loop quantum cosmology' Date and Hossain...
  47. H

    Negative energy density in a Casimir vacuum

    I have read often that the vacuum energy density in a Casimir vacuum is negative, but I do not understand this. My understanding is the following. The Hamiltonian can be written as a sum over all spatial modes. Calculating the energy density for the vacuum state H|0> = ∫dV ρ_o |0>, leaves...
  48. B

    Solving a Fields Exam Challenge: Calculating E Field & Energy Density

    Okay I've got a fields exam coming up so like a good boy I've been practising with past papers :wink: but there is this one question that is driving me batty :confused: a) Consider a long cylindrical co-axial capacitor with inner conductor radius a, outer conductor radius b, and a...
  49. H

    Accepted value for Omega of radiation energy density

    What is the currently accepted value for Omega of radiation energy density (photons and neutrinos)? References would be helpful. Thanks.
  50. H

    Vacuum energy density and Hubble expansion

    This may be a simple question but I didn’t found anything in my references: the vacuum energy density is a constant value, which depends on the virtual excitations of the quantum fields. If the universe expands, increases its volume, and the vacuum energy density remains is constant, does this...
Back
Top