What is Expansion: Definition and 1000 Discussions

Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.Temperature is a monotonic function of the average molecular kinetic energy of a substance. When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves. Substances which contract with increasing temperature are unusual, and only occur within limited temperature ranges (see examples below). The relative expansion (also called strain) divided by the change in temperature is called the material's coefficient of linear thermal expansion and generally varies with temperature. As energy in particles increases, they start moving faster and faster weakening the intermolecular forces between them, therefore expanding the substance.

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  1. Ahmed Abdalla

    Why do we use Taylor expansion expressing potential energy

    My textbook doesn’t go into it, can someone tell me why Taylor expansion is used to express spring potential energy? A lot of the questions I do I think I can just use F=-Kx and relate it to U(x) being F=-Gradiant U(x) but I see most answers using the Taylor expansion instead to get 1/2 kx^2...
  2. MathematicalPhysicist

    Derivation of the expansion of the potential in rectangular coordinates

    Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...
  3. D

    Taylor expansion fine structure

    I have to do a Taylor expansion of the energy levels of Dirac's equation with a coulombian potential in orders of (αZ/n)^2 , but the derivatives I get are just too large, I guess there is another approach maybe? This is the expression of the energy levels And i know it has to end like this:
  4. S

    I Asymptotic expansion integral initial step

    Consider the integral $$ G(x) = \int_0^\infty \frac{e^{-xt}}{1+t}dt$$ which is convergent for x>0. For large x, it is dominated by small t so expand: $$G(x) = \int_0^\infty e^{-xt}\sum_{m=0}^{\infty}(-t)^mdt$$ From here my notes say to take out the summation and write: $$G(x) =...
  5. Z

    Reversible Isothermal Expansion Steam

    Homework Statement 2kgs (total mass) of steam goes through a revesible isothermal expansion at 500 degrees celcius. During the expansion the pressure drops from 300 kpa to 200 kpa. What is the heat absorbed by the steam during this process? Homework Equations U=W and W=nrt ln(v2/v1) The...
  6. mertcan

    A Taylor Expansion of Metric Tensor: Troubles & Logic

    Hi, my question is related to taylor expansion of metric tensor, and I have some troubles, I would like to really know that why the RED BOX in my attachment has g_ij (t*x) instead of g_ij(x) ? I really would like to learn the logic...
  7. R

    Size expansion vessel to reduce pressure loss

    Hi all, Given: I have a pressure vessel of 1000M^3 filled with water with 8 bar pressure. On this pressure vessel I have installed a valve and a expansion vessel on top of the pressure vessel. The expansion vessel is prepressurized to 8 bar as well. Question: when I open the valve i lose 20...
  8. D

    Is the Entropy in a Free Expansion Affected by the Gas Type?

    Homework Statement The question is: What happened with the entropy in a free expansion? The system is isolated and the state equation is: $$p=AT/V+B/V^2$$ Homework Equations $$dU=TdS-pdV$$ The Attempt at a Solution My attempt is: Because the system is isolated and corresponding to an free...
  9. S

    A Taylor expansion of dispersion relation - plasma physics

    Hello, I may working through attached paper and really need help with deriving equation in appendix - A4 to give A10. http://iopscience.iop.org/article/10.1088/0004-637X/744/2/182/pdf Any help would be greatly appreciated. thanks, Sinéad
  10. bdolle

    What is the Correct Way to Write a Binomial Expansion for (1+(1/x))^(-3/2)?

    <Moderator's note: Moved from a technical forum and therefore no template.> Hey All, For my modern physics class we were told to write out a binomial expansion of (1+(1/x))^(-3/2). I am fairly confident in the work I did, but my professor posted his work and it is different and way simpler...
  11. Grinkle

    B Expansion Propagation: Finite Seed vs Everywhere?

    Is there any theory to say if expansion started with a finite seed and propagated out at a finite speed vs somehow happening everywhere at once? I know the layman's phrasing is that expansion happened everywhere at the same time. That might just mean that the very small part of the early...
  12. mertcan

    A Christoffel symbols expansion for second derivatives

    Hi, I really wonder how these second derivatives can be written in terms of christofflel symbols. I have made so many search but could not find on internet What is the derivation of equations related to second derivatives in attachment?
  13. mertcan

    I Taylor expansion of 1/distance

    Hi, I would like to express that r and r' are vectors in the attachment and let's say that r is observer distance vector r' is source distance vector. By the way I know this is taylor expansion (for instance if there was only x component (scalar form) I would not any ask question ). But I do...
  14. T

    I Is Expansion the Same as Contraction?

    How do you tell the difference of expanding outwards and contracting inwards? Part of my intuition tells me that it would be impossible to tell the difference. If you are on the natural numbers heading from zero to infinity I might say that is expanding outwards. So if you are sitting at...
  15. I

    B A thought on the expansion of the Universe

    One thing that has always puzzled me is that the farther we look out into the universe we see that galaxies are moving away from us faster than galaxies that are closer to us, but also the farther we look out into space the farther back in time we are observing. I have trouble understanding...
  16. H

    I How fast is the Universe expanding?

    hello there, I am totally into all astrophysics. so I want to know, how fast is the known universe at the most outer edge moving? or in other words, how fast is the most outer edge expanding away from earth. - and what's the rate of acceleration? I mean even if, as I understand it, the space...
  17. R

    I Amplitudes of Fourier expansion of a vector as the generalized coordinates

    When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...
  18. B

    B What is the reaction to gravity's pull in a vacuum?

    I am trying to understand something. Let me pitch a scenario: You have two asteroids in a vacuum. Each is large enough to be round by gravity. They are separated by roughly the distance from the Earth to the moon. Relative to each other, they are moving at 0 in all directions (aka, they are...
  19. P

    I IOAA 2nd problems: universe expansion

    Could anyone please guide me how to do these problems?
  20. D

    Van der Waal expansion and delivered work

    Homework Statement Assume that one mole of an ideal van der Waals fluid is expanded isothermally, at temperature T_h from an initial volume V_i to a final volume V_f. A thermal reselvoir at temperature T_c is available. Apply dW_{RWS} = \left ( 1 - \frac{T_{RHS}}{T} \right ) (-dQ) +(-dW) to a...
  21. E

    Calculate Pressure Drop through Expansion/Reduction for Gas

    Something that routinely comes up as a problem at work is when we size flow projects for piping systems. We calculate pressure drop across a length of fixed diameter for compressible gasses, but we do not calculate pressure changes through an expansion or contraction with gas (for example...
  22. Mr Davis 97

    Finding Maclaurin expansion and interval of convergence

    Homework Statement Find the Maclaurin series and inverval of convergence for ##f(x) = \log (\cos x)## Homework EquationsThe Attempt at a Solution I used the fact that ##\log (\cos x) = \log (1+ (\cos x - 1))##, and the standard expansions for ##\cos x## and ##\log (x+1)## to get that...
  23. R

    B Special relativity and expansion of the Universe, A paradox

    Consider two bodies A &B are moving apart with a velocity V due to the expansion of space. According to an observer in A the body B is moving away and an observer in B feels the body A is moving apart. Can some one answer in which body the time dilates and why?. ( I am specifying once again that...
  24. K

    B Why Is My Second Derivative Calculation for Taylor Expansion Incorrect?

    So in the book it says expend function ƒ in ε to get following. ƒ=√ (1 + (α + βε)2) = √ (1 + α2) + (αβε)/√ (1 + α2) + (β2ε2)/2 (1 + α2)3/2 + O(e3) When I expend I get(keeping ε = 0) ƒ(0) = √ (1 + α2) -->first term ƒ'(0) = (αβ)/√ (1 + α2) --> sec term with gets multiplied by ε for third...
  25. chopnhack

    Solving Volumetric Expansion of Water in Glass

    Homework Statement An ordinary glass is filled to the brim with water at 100oc. How much water could be added to the glass if the temperature is lowered to 20oC? Assume that the coefficient of volume expansion for glass is 2.7 x 10-5 K-1 and for water it is 2.1 x 10-4 K-1.Homework Equations ΔV...
  26. A

    Electromagnetic Ring Expansion Test

    If my professor tasked me with finding out where to find the materials for setting up an electromagnetic ring expansion test, where is a good place to start? Generally, what is a good procedure to follow when setting up an experiment? I am not very experienced but I would like to learn. The...
  27. F

    I Calculating Perturbative Expansion of Metric Inverse in Cosmology

    As I understand it, in the context of cosmological perturbation theory, one expands the metric tensor around a background metric (in this case Minkowski spacetime) as $$g_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$$ where ##h_{\mu\nu}## is a metric tensor and ##\kappa <<1##. My question is, how...
  28. mohau tshekoeng

    B Is the concept of a multiverse just science fiction or a scientific possibility?

    It is been said that the universe is expanding but the question is,where will the universe end? Are we the only universe?
  29. C

    I Neutrino flavour eigenstates and expansion of the universe

    Neutrinos were flavor eigenstates at the time of their decoupling from baryonic matter. Since they were not pure mass eigenstates, how do you take this fact into account if you try to study how they evolved as the universe expanded? Could we determine if the heaviest neutrino could be non...
  30. C

    Can I use thermal expansion to hold together materials?

    Okay, I will give a quick run down of what I am trying to do here. What I want to do is build a tesla turbine from old hard drive disks. Being that they're already rated for high RPM, it seems like a viable option. Now these disks are probably going to be aluminum and I am probably going to buy...
  31. PHstud

    Liquid to gas expansion temperature change in a tank

    Hello ! I have troube doing a calculation. Let's say we have a volume Vi in a tank at a pressure Pi. If I let my tank open, the tank's liquid will start to boil to keep the pressure Pi inside the tank. Now, at the end, I will have a volume Vf in the tank, and still a pressure Pi. But the...
  32. M

    B Dark Energy & Expansion of Spacetime

    PLEASE BE ADVISED: I'm a complete ignorant with regards to the details of what I'm about to say and I've never looked at the mathematics of the subject, let alone understand it. So most of what I am about to say comes from pop science. Excuse me in advance if I sound stupid or rhetorical...
  33. E

    Linear expansion by heat for an object

    Homework Statement http://i.imgur.com/swYr8aw.jpg Homework Equations delta L=LalphadeltaT The Attempt at a Solution sorry for s**ty handwriting look at #8[/B] http://i.imgur.com/59Ew8vJ.jpg edit:click the links please. The forum software cropped the quality of the photo.
  34. Addez123

    B Does red-shifted light cause expansion of space?

    Light can get red-shifted due to expansion of space, this leads to a loss of energy. Would it be possible that this energy is what's causing the universe to expand in the first place?
  35. S

    A Perihelion Precession in GR with Robertson Expansion

    In his book Gravitation and cosmology, Weinberg derives the perihelion precession of Mercury in the Robertson expansion. The final formula is \Delta\phi =\frac{6\pi M G}{L} \frac{2+2\gamma-\beta}{3} The second term is one for GR (β=γ=1). I have two questions regarding this formula: 1. The...
  36. M

    Internal Energy of virial expansion

    Hello, I have some trouble understanding the virial expansion of the ideal gas. 1. Homework Statement I have given the state equation: $$ pV = N k_b T \left(1+\frac{A\left(T\right)}{V}\right) $$Homework Equations [/B] and a hint how to calculate the caloric equation of state $$...
  37. binbagsss

    Laurent series expansion of ℘(z).

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] Hi, I am trying to understand the 2nd equality . I thought perhaps it is an expansion of ##(1-\frac{z}{w})^{-2}## (and then the ##1## cancels with the ##1## in ##( (1-\frac{z}{w})^{-2}) -1 ) ##) in the form ##(1-x)^{-2}##...
  38. A

    Thermal Expansion: Volume vs. Linear - 0.11L Spilled

    Homework Statement A one-liter pot is completely filled with oil. Heat is applied to the pot&oil and the temperature rises from 15°C to 190°C. How much oil is spilled over? The linear coefficient of thermal expansion for oil is 0.68*10-3; the one for the pot is 2.4*10-5 Homework Equations...
  39. yecko

    Maximizing Integration Expansion | Homework Solution

    Homework Statement https://holland.pk/uptow/i4/d6adf6b4297ef9c8c20c3e58ec66535d.png Homework Equations integration The Attempt at a Solution [/B] https://holland.pk/uptow/i4/36ea9fcf0a17f1ea8137f0140c881289.jpg I have got stuck at this step... And have no idea on how to go on to the...
  40. S

    A Multipole expansion of linearized field equations

    I read Chris Hirata's paper on gravitational waves (http://www.tapir.caltech.edu/~chirata/ph236/lec10.pdf) where he performs a multipole expansion of the gravitational source. I got most of it, apart from the part where he expands the inverse distance function into a series : More specifically...
  41. V

    B Exploring the Expansion of Space & Time

    We are told that space is expanding and that the rate of expansion is speeding up. However, as relativity shows that space and time are inextricably linked, does this mean that time is expanding too?
  42. H

    Thermal expansion of each dimension of a solid

    Hi, I am trying to work out how much each dimension of a solid (for instance an annular disc) made out of steel changes assuming that the solid is heated uniformly and is not constrained at any of its boundaries. Am I right in saying that, the linear expansion equation L = L_0 (1+ α ΔT) can be...
  43. G

    Thermal Expansion of A-36 Steel Rails: -20F to 90F

    Homework Statement The 40 ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap in inches so that the rails just touch one another when the temperature is increased from -20 F to 90 F. The cross sectional...
  44. T

    I Expansion of Plane of Projection: Terrel & Penrose

    In two papers of Terrel and Penrose, the concept of Terrel effect were presented. Both of the papers say that "the plane of projection is expanded by a certain factor, which is equal to Doppler factor for certain cases." Now does it mean the area of the projected plane is expanded by that...
  45. O

    Control Volume of single expansion ramp nozzle (SERN)

    Hi guys, I need to determine the performance of a single expansion ramp nozzle (SERN) from CFD results with different nozzle pressure ratios (NPR). For some NPR the nozzle is overexpanded and for some underexpanded. Now the impact of the control volume definition on especially the axial thrust...
  46. C

    Alternate Heat Expansion Media for Nuclear Power Plants

    I am interested in whether it might be possible to select a more efficient heat expansion media for nuclear power plants than water, which has a very specific heat and a very high heat of vaporization. The high value of the specific heat and the heat of vaporization of water requires much...
  47. N

    I Do particles create space over time? Is that expansion?

    If a particle can potentially be transported to any place in space limited only by the speed of light, does that potential amount to an expansion of space? And another question: Does it make sense to define space as any place a particle could go to?
  48. durant35

    I Does the number of causal patches increase bc of expansion

    I'm having a hard time understanding some fundamental properties of our expanding universe. It seems reasonable that globally the size of the universe increases bc of the expansion. However the size of each causal patch/observable universe stays the same. Following this logic it would seem that...
  49. Vitani11

    How do you find the fourier expansion coefficients?

    Homework Statement I need to expand this piecewise function f(x) = h for a<x<L and f(x) = 0 for 0<x<a. I am told that this is a square wave so ao and an in the expansion are 0 (odd function). Therefore I only need to worry about bn. The limits on the integral are from a to L, but what about the...
  50. Buzz Bloom

    A A cosmological expansion problem too difficult for me

    I began thinking about the problem I describe below from trying to understand the discussions in another thread. https://www.physicsforums.com/threads/concordance-cosmology-paper.909603 This problem is about the expansion behavior of a “simple” universe model that might demonstrate a distinction...
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