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. M

    Is expansion actually slowing?

    New member here, thanks for your patience. The farthest galaxies are the most redshifted, but doesn't that old light tell us more about the rate of expansion closer to the beginning of the Universe?
  2. marcus

    Cosmology's sole "rate of expansion" is declining

    In a quantitative science verbal phrases like "rate of expansion" have to correspond to mathematically well-defined quantities. As far as I know, in Cosmology the only quantitative handle in common use that corresponds to "rate of cosmic expansion" is the Hubble constant, and as best we can...
  3. B

    Thermal coefficients of expansion

    Homework Statement A brass rod (linear expansion coef 19*10-6/°C) has a radius of 8139 cm and a copper (linear expansion coef 17*10-6/°C) sheet has a hole or radius 8139+8.86cm. What temperature change (K) is required to close the gap? Homework Equations ΔL/Lo = αΔT? The Attempt at a Solution...
  4. L

    Metric expansion misunderstanding

    Here is the second paragraph from the article on metric expansion of space from Wikipedia Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the FLRW metric, and is a generic property of the Universe we inhabit. However, the model is valid only on large...
  5. D

    Vacuum: Potential Energy & Universe Expansion?

    If I induce vacuum in a glass tube and then I open the lid of the glass tube, air rushes into fill in the vacuum. Can vacuum be regarded as a sort of potential energy, able to exert a force? Can a vacuum tube be considered as a potential storage device for energy, just like a container filled...
  6. halpmaine

    Expansion then Contraction....an infinite Elastic Collision?

    Wouldn't the explanation that fits fundamental laws (e.g. Conservation of E) while making the least asumptions be an ongoing bang-crunch-bang...scenario? Why couldn't expansion be eventually reigned in by forces, dark matter and the like - ultimately leading to contraction? Why shouldn't...
  7. H

    Question about reversible adiabatic expansion

    Hello guys, I have some troubles to understand a reversible adiabatic expansion. we have dq=0 and dw=-pdV and for a perfect gas dU= Cv*dT. I don't really understand why dU= Cv*dT since we have a variation of volume and it is established that dU= Cv*dT when we haven't any modification of the...
  8. A

    Understanding the Expression (16) in Kohn Sham Energy Expansion

    Can anyone help me understand how to arrive at the expression (16) in the following link? http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-50532009000700002&lng=en&nrm=iso&tlng=en I don't see how it follows from insertion into (14), but I have seen exactly this transition happen...
  9. ShayanJ

    Unbounded operator and expansion of commutator

    Consider two self-adjoint operators A and B with commutator [A,B]=C such that [A,C]=0. Now I consider an operator which is a function of A and is defined by the series ## F(A)=\sum_n a_n A^n ## and try to calculate its commutator with B: ## [F(A),B]=[\sum_n a_n A^n,B]= \\ \sum_n a_n...
  10. RJLiberator

    Finding expansion coefficients of a generic vector?

    Homework Statement Find the expansion coefficients of a generic vector (λ, μ) ∈ ℂ^2 in the orthonormal basis: { i/sqrt(2) (1, 1), 1/sqrt(2) (1, -1) } Homework Equations λ_i = |v_i> |v> The Attempt at a Solution I don't think this should be difficult. But, clearly, as I am posting here, I do...
  11. P

    I Contraction prior to expansion?

    A number of contemporary models propose that the universe was contracting prior to expansion. However I have found this critique of such a proposal from Geroge Elliss: “initial conditions have to be set in an extremely special way at the start of the collapse phase … in an acausal way (in the...
  12. Pejeu

    Spaghettification and gravity in theory of relativity?

    Per my layman's understanding, the apparent force of gravity, as explained by the general theory of relativity, is actually the result of rectilinear motion at uniform speed through warped spacetime. 1. If that's the case, what actually causes gravity for objects at rest with respect to the...
  13. D

    Calculating Thermal Expansion of Water: Is the Formula Correct?

    Hello, I'm trying to determine a way of calculating the thermal expansion of a volume of water. The formula I have come across is: ΔV = βV0ΛT The general consensus seems to be that water expands roughly 4% from 20°C to 100°C, or 4.2% from 4°C to 100°C...
  14. ShayanJ

    Expansion of the solution if interacting KG equation

    The exponentials ##\phi_p(x)=e^{ipx} ##(where ## px=p_\mu x^\mu##), are solutions of the free KG equation ## (\partial_\mu \partial^\mu+m^2) \phi =0##. I can expand the solutions of the interacting KG equation ## (\partial_\mu \partial^\mu+m^2)\psi=V\psi ## in terms of solutions of the free KG...
  15. Geofleur

    What causes temperature changes in Joule's expansion experiment?

    In his book, Theoretical Concepts in Physics, Malcolm Longair describes two experiments that Joule performed involving gas expansion (the discussion starts on pg. 217). In both experiments, there is a chamber containing gas, labeled A, and a chamber that is evacuated, labeled B. There is also a...
  16. S

    Taylor expansion of the square of the distance function

    Does it make a sense to define the Taylor expansion of the square of the distance function? If so, how can one compute its coefficients? I simply thought that the square of the distance function is a scalar function, so I think that one can write $$ d^2(x,x_0)=d^2(x'+(x-x'),x_0)=d^2(x',x_0) +...
  17. Korbid

    Virial expansion: Resolving these integrals

    Hi! From this text: http://arxiv.org/pdf/nucl-th/0004061v1.pdf I need to resolve these integrals. 1) Equation (5), \int e^{-\omega_1/T}d{\vec k}_1 =? where \omega_1=\sqrt{m^2+{\vec k}^2_1} What function is K_2(m/T)? 2) Equation (26), \rho_s(T) Thanks!
  18. C

    Relationship Between V and T in Adiabatic Expansion

    Homework Statement The energy and pressure of black body radiation depend on T and V as Eq(1) & Eq(2). Suppose that the temperature and volume of a box of radiation change adiabatically. Find the relation between dE and dT in this process. Next, using Eq(1), show that T ∝V^-1/3 Homework...
  19. A

    Calculating reversible adiabatic expansion

    I have some homework that I am just not able to figure out. There is a 2kg parcel of air at T1=32°C and p1= 0.8 atm This parcel of air expands until it is at T2=12°C Also, during the expansion 3.2 g of water will condense due to the dT (ΔvapH (water) = 40.65kJ mol-1 Also: Cv=0.718 kJ...
  20. R

    (Thermo) Energy as Taylor expansion

    Homework Statement [/B] I've attached a screenshot of the problem, which will probably provide much better context than my retelling. I'm having problems with parts f and g. The most relevant piece of information is: "To get used to the process of Taylor expansions in two variables, first we...
  21. T

    Universe Expansion: What are the Limits?

    Hi, We all know the universe is expanding and it's doing so at a rate greater than the speed of light. But what does expansion mean? Popular Science videos usually give the loaf of bread example expanding in the oven. But even the loaf of bread has limits, it can only expand so far. Do we know...
  22. Passionate Eng

    Is the Milky Way at the center of the expanding universe?

    I read in "The Theory of Everything" of Stephen Hawking that all of the galaxies are running away from ours. That made me think that the Milky Way is the center of universe, since each galaxy is running away from us(like waves on the surface of water centered at one point which is the Milky...
  23. C

    Hydrogen atom state expansion

    Homework Statement [/B] Consider a hydrogen atom which, in t = 0, is in the state given by \psi(\mathbf{r},t>0)=\frac{A}{4\pi}R_{10}(r)+\frac{cos\alpha}{4\pi}\left(\frac{z-\sqrt{2}x}{r}\right)R_{21}(r) Expand ψ in terms of the {Φnlm} basis of normalized eigenfunctions...
  24. M

    How do I Solve for A in Partial Fraction Expansion?

    Homework Statement divide in partial fractions: x^3 -3x^2+x-12 / x^4+5x^2+4 Homework EquationsThe Attempt at a Solution I factored x^4+5x^2+4 to (x^2 +1) (x^2+4) x^3 -3x^2+x-12/(x^2 +1) (x^2+4) = A (x^2+1)/(x^2 +1) (x^2+4) + B (x^2+4) /(x^2 +1) (x^2+4) they all have the same...
  25. H

    Can the Universe's Acceleration be Measured in m/s^2 Instead of m/s/pc?

    Is it possible to measure the universe' expansion in m/s^2 instead of metres per second per parsec?
  26. S

    Riemannin generalization of the Taylor expansion

    I thought about the Taylor expansion on a Riemannian manifold and guess the Taylor expansion of ##f## around point ##x=x_0## on the Riemannian manifold ##(M,g)## should be something similar to: f(x) = f(x_0) +(x^\mu - x_0^\mu) \partial_\mu f(x)|_{x=x_0} + \frac{1}{2} (x^\mu - x_0^\mu) (x^\nu -...
  27. Jimster41

    The Impact of Cosmological Expansion on the Planck Length: A Quantum Perspective

    I get that Planck length is derived from h, G and c. But as a theoretical measure of length how is it affected or not affected by cosmological expansion?
  28. Johnny Neutrons

    Black hole expansion in the LHC?

    Greetings, I am new to this forum and would like to present a discussion. If a miniscule black hole is created in the LHC. Is it probable the LHC is capable of creating more than one black hole during a single event collision? Considering fact and theory provided by credible research. Could...
  29. samsara15

    Where does photon energy go in universe expansion?

    [Moderator's note: Spun off from another thread, where it was off topic. Please start a new thread when you have questions on a new topic.] Photons lose energy when they travel long distances. Where does that energy go? What happens to that energy? Is there any theory regarding this?
  30. B

    Fourier series expansion problem

    < Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown > hi I've got a problem that I've partially worked but don't understand the next part/have made a mistake? f(x)=0 for -π<x<0 and f(x)=x for 0≤x≤π i got a0=π/4 and an=0 and bn=0 if n is even and 2/n if n...
  31. D

    Does Space Expansion Add Potential Energy?

    Space is expanding, which separates objects from each other in space. Won't this add potential energy? Doesn't this violate the law of conservation of energy? But if it does not, how can space be added without adding potential energy?
  32. Jorrie

    Insights Approximate LCDM Expansion in Simplified Math (Part 4) - Comments

    Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math (Part 4) Continue reading the Original PF Insights Post.
  33. ash73

    How is expansion manifested physically?

    Hi, newbie reading the forum with interest, and trying to understand how expansion manifests itself physically. Four possibilities; 1. New space is created between existing space, pushing galaxies apart 2. Existing space is stretched, pushing galaxies apart 3. Empty space is nothing, and...
  34. Glurth

    Describe the mechanism in GR causing *Space* expansion

    From what I have read, it sounds like GR predicts that under certain conditions, space itself will expand. If this is incorrect, please just let me know and ignore the below. While I don’t know the math involved in GR, I can understand explanations of how gravity distorts space-time, to alter...
  35. H

    Thermal Expansion of Two Holes

    I have a problem understanding the concept of thermal expansions of solids with a hole in it. I do not want to accept face value the traditional explanation i am given that hole will increase in size because i am told to imagine if the hole was never cut. I fail to see the congruency in these...
  36. S

    Relation between thermal expansion and density in Polymers

    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...
  37. Dry

    Expansion is a compounded error based on a wrong assumption?

    I accept that what I write below will be unpopular and argued with vehemently, however I think it should be considered with an open mind and recognised for the sense that it has. Originally the concept of an expanding universe (and therefore by extrapolation the concept of the Big Bang that...
  38. Jorrie

    Insights Approximate LCDM Expansion in Simplified Math (Part 2) - Comments

    Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math (Part 2) Continue reading the Original PF Insights Post.
  39. Shankar Dev

    Does theory of expansion effect gravity?

    If space will be expansion then it effect on Earth diameter. If Earth become narrow then how gravity force work ?
  40. Strilanc

    Does the Hubble expansion of space have a preferred frame?

    I have a paradox that I don't know the answer to. Special relativity has no preferred frame, but it seems like adding an exponential expansion to space introduces such a frame. The Setup Suppose we're in a universe with a much faster expansion rate, where the space between any two objects...
  41. I

    Finding the Limit of a Sequence with Taylor Expansion and Exponentials

    Homework Statement Let ##x_n## be the solution to the equation ##\left( 1+\frac{1}{n} \right)^{n+x} = e## Calculate ##\lim_{n\to \infty} x_n## Homework Equations N/A The Attempt at a Solution Since ##\lim_{n \to \infty} \left(1+ \frac{1}{n} \right) = e## that tells me that ##\lim_{n\to...
  42. Jorrie

    Insights Approximate LCDM Expansion in Simplified Math - Comments

    Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math Continue reading the Original PF Insights Post.
  43. O

    Big Bang Expansion Creates Planets?

    If I understand what the BB Theory proposes, all the universe was originally confined to the size of something very small, like a dot or an atom. This small dot or atom or whatever was said to explode, although some say there was no explosion in the sense of a bomb going off, but would be more...
  44. A

    Comparing Coefficients of Thermal Expansion in Solid Rods

    Homework Statement the difference in length between an aluminium rod and a copper rof at 0 degreeC is 2cm. If they have the same difference in length at any temperature difference, what are the length of the 2 rods at 0 degreeC.? Al - expansivity = 20*10^-4 K^-1 Cu- expansivity= 15*10^-6 K^-1...
  45. B

    Confused - Pressure in a canister?

    A manufacturer quotes a standard CO2 canister contains 16g of CO2 at a volume of 20cm^3. So I need to calculate the pressure in the canister... Using ideal gas law P = nRT/V n = 0.364mol (16 of co2) R = 8.314 J/Kmol (universal gas constant) T = 294k (gas is at room temp 21 deg C) V = 20cm3...
  46. ComaBerenices

    Proportions and other Stuff about Expansion

    I'm not too well read in cosmology, but I know the universe is presumed to be homogeneous in space but not in time, therefore the curvature of the universe can essentially be calculated under one mean. I just have a few questions about how the universe expands and whether some proportions are...
  47. G

    Does space expansion affect the rate of time?

    Time can have 2 different connotations. One is inherent to an entity in spacetime by itself, say a lonely radioactive atom. It may decay or it may not decay, independently of what's going on around it. But another involves interactions between particles, for example "it takes 60 seconds for...
  48. ognik

    MHB Simplifying Binomial Expansion for Relativistic Velocity Sum

    Hi, given the sum of 2 relativistic velocities $ \frac{w}{c} = \frac{\frac{u}{c}+\frac{v}{c}}{1+\frac{uv}{c^2}}$ and setting $ \frac{u}{c}= \frac{v}{c} = (1-\alpha)$, find $ \frac{w}{c} $ in powers of $ \alpha $ through $ {\alpha}^{3} $ I used a binomial expansion to get a tidy intermediate...
  49. P

    Gimbal Joint analysis (Thermal expansion)

    Good day, I am currently developing a thermal expansion analysis of a pipe line, I need to validate if the current installed Gimbal joints will withstand those conditions. These gimbal joints just allow angular movement. Is there any software or method that can help me as reference for this...
  50. **Mariam**

    Calculating linear expansion of windshield 60cm*150cm

    Homework Statement An automobile windshield has the dimensions 60cm by 150 cm. What minimum tolerance is needed in mm to prevent the windshield from breaking if the temperature changes by 200F (the linear expansion coefficient of glass is 9*10^-6 C-1) Homework Equations deltaL=alpha*Li*deltaT...
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