Expansion Definition and 1000 Threads

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. T

    Is the expansion of the universe similar to an explosion?

    Even though the big bang wasn't an actual explosion per se it did have the expansive characteristic of an explosion right? At some point in time during the expansion two bodies might be x distance apart. A little farther down the timeline those same two objects would be farther from each other...
  2. virgil1612

    Expansion of space in our neighborhood

    I know that expansion of space operates farther away from our Local Group of galaxies. But the reason for not considering expansion in our galactic neighborhood is: A. The space expands everywhere, the expansion is just too small close to us so we don't need to talk about it. or B. The space...
  3. M

    Linear and Volume Expansion problem

    Homework Statement An aluminium container (cylinder) is filled with glycerine. Glycerine has a volume expansion coefficient of 4.85 × 10^-4 (°C)-1. Aluminium has a linear expansion coefficient of 2.40 x 10^-5 (°C)-1. At a temperature of 20.00°C the scale on the side of the aluminium container...
  4. Ghostcrown

    Can the expansion of space affect the speed of light?

    If the space between any two objects is expanding at a rate faster than light itself can travel, how is it that we're observing light from things so far away? One would think that the expansion of space affects light too, such that the space between the emitted light and the destination of said...
  5. R

    Expansion of the exponential function

    Please delete, got mixed up, apologies.
  6. D

    How do I write taylor expansion as exponential function?

    How do I write taylor expansion of a function of x,y,z (not at origin) as an exponential function? Please see the attached image. I need help with the cross terms. I don't know how to include them in the exponential function?
  7. AdityaDev

    Summation with binomial coefficients question

    Homework Statement ##\sum\limits_{r=0}^n\frac{1}{^nC_r}=a##. Then find the value of $$\sum\sum\limits_{0\le i<j\le n}(\frac{i}{^nC_i}+\frac{j}{^nC_j})$$ Homework Equations I have used two equations which I derived myself. This is the first one. The second one is: 3. The Attempt at a...
  8. Ahmed Nabi

    Where Does Earth's Counter Gravity Go in an Expanding Universe?

    Hi everyone! I am new to cosmology and have come across this unbelieving interesting field quite recently ( after reading 'A Brief History of Time' to be honest ). This is my first post in PF. Hubble first discover that the universe is expanding with non-constant, accelerating velocity. Also...
  9. N

    Multinomial Expansion: Solve (Σ^m_i x(i) Σ^i_j x(i,j))^n

    Hi, I would like to express the following formula in terms of a straightforward multinomial expansion: (Σ^{m}_{i=0}x(i)*Σ^{i}_{j=0}x(i,j))^n Any help would be useful.
  10. mike l

    Hydrogen oxygen ignited volume expansion

    Homework Statement there is an expandable container with 1m3 of hydrogen and 1/2 m3of oxygen at stp. the gas is ignited.what is th final volume if there is no heàt lost and the pressure outside the container is 1atm? assume complete combustion Homework Equations other than the ideal gas...
  11. D

    Entropy change of van der Waals gas expansion

    Homework Statement Consider ##n## moles of gas, initially confined within a volume ##V## and held at temperature ##T##. The gas is expanded to a total volume ##\alpha V##, where ##\alpha## is a constant, by a reversible isothermal expansion. Assume that the gas obeys the van der Waals equation...
  12. S

    Can Expanding Space Overcome Quark Confinement in Particles?

    This thread involves a little general relativity and a little particle physics. Observations indicate that space is expanding at an accelerated rate. Given this would continue, even atomic nuclei should be torn apart leaving single particles, isolated from one another by causal horizons. What...
  13. R

    Irreversible adiabatic expansion in which P_ext=0

    Homework Statement In an adiabatic irreversible expansion of ideal gas , if Pext = 0 then which is true, A. T2=T1 B. Q=0, C. P1V1= P2V2 D. P1V1γ= P2V2γ Homework Equations ΔU = Q - W For ideal gas, PV= nRT[/B] ΔU ∝ ΔT The Attempt at a Solution I know Q= 0, Work done is zero, So ΔU = 0, hence...
  14. C

    Does cos(sqrt(x)) have a valid Taylor series expansion at a=0?

    Find the Taylor series about a=0 for the function F(x) = \cos(\sqrt{x}). Taylor series expansion of a function f(x) about a \sum^{\infty}_0 \frac{f^{(n)}(a)}{n!}(x-a)^n Taylor series of \cos{x} about a=0 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} \ldots From these...
  15. AlexDB9

    FTL Expansion of Space: Rapidity & Infinity

    If the expansion of space in the macrolevel is faster than the speed of light then it should have "more" than infinite rapidity. How does that work out? Thanks.
  16. F

    Unitary translation operator and taylor expansion

    Homework Statement I have quite a straightforward question on the taylor expansion however I will try to provide as much context to the problem as possible: ##T(a)## is unitary such that ##T(-a) = T(a)^{-1} = T(a)^{\dagger}## and operates on states in the position basis as ##T(a)|x\rangle =...
  17. SpiderET

    Acceleration of expansion of Universe not that fast?

    There is some surprising twist regarding measurements of accelerating expansion of Universe. Maybe it is not accelerating that fast as previously predicted. It seems that there is something questionable about Ia supernovae. What do you think about it? Is this real game changer or some minor...
  18. N

    Mathematica code for multinomial expansion

    Hello, I m looking for a mathematica code for the multinomial expansion of the general case of (let's say m sum terms given in a power of n), e.g., the code for the 1st equation in http://en.wikipedia.org/wiki/Multinomial_theorem Any help would be useful. Thanks
  19. V

    MATLAB Simulating Plane Wave Expansion in Matlab

    Dear Sir Madam, I am a new member of this forum and I was trying to understand Plane Wave expansion simulation in Matlab. So far I cannot understand how to simulate Gz vector in K-space consistently to the numbers of plane waves. Hereby you can have the MATLAB code for Gx and...
  20. P

    How Does Temperature Affect the Density of an Object?

    Homework Statement An object has a density of 1250 kg /m3 at 10◦C and a coefficient of linear expansion of α = 2.5 × 10−5 1 /K . What is the object’s density when the temperature is 25◦C?Homework Equations V=βV0ΔT V(T)=(1+β(Δt))V0 The Attempt at a Solution How I got the answer is that I used...
  21. P

    Thermodynamics question: density, linear expansion and temperature

    An object has a density of 1250 kg m3 at 10◦C and a coefficient of linear expansion of α = 2.5 × 10−5 1 /K . What is the object’s density when the temperature is 25◦C? I have tried using the equation ΔL=αL° ΔT but this equation has nothing to do with density. the answer should be: 1248.6 Your...
  22. L

    Multipole Expansion: Understanding Electric & Magnetic Fields

    Hello, I was hoping someone could help make the concept of electric multipole/ magnetic multipole expansions clearer. I think my most fundamental question is: Are dipole, quadrupole and up fields just a shortcut to using the superposition principle on a charge distribution in space or do they...
  23. A

    How Does Adiabatic Expansion Lead to Condensation?

    Homework Statement In an earlier part of the question, I derived the temperature dependence of the latent heat of vapourisation of a liquid as dL/dT=L/T+ΔCp-L/Vvap(∂Vvap/∂T)p I am asked to find the condition that upon expanding the gas adiabatically, we get condensation to occur, by considering...
  24. J

    What happens to the absorbed mass in a collapsing black hole?

    So I was reading threads and i came across a question on what happens when a black hole collapses. As I was reading the responses, I saw some people commenting in which they asked if the mass the black hole absorbed was released when the black hole collapsed. If it did would the black hole...
  25. P

    Change in internal Energy During Expansion of an Ideal Gas

    Homework Statement Derive an expression for the change in internal energy of 1 mol of an ideal gas for expansion from volume V_i to V_f under constant pressure of 1atm where \gamma = \frac{C_p}{C_v}=\frac{5}{3} Homework Equations \Delta U=\frac{3}{2}nR\Delta T PV=nRT The Attempt at a...
  26. P

    Cosmic expansion in quantum gravity

    Ive often heard that in quantum gravity space time is discrete. One analogy I've heard is to think of spacetime as being made up on space time atoms. In these models when the universe expands, is the number of space time atoms thought to increase?
  27. V

    Increase of dark energy with expansion of universe

    Why does dark energy increase along with the expansion of the universe ( I'm not even sure it does but if it dosen't please correct me :))
  28. B

    Reversible and Irreversible Expansion

    What's the difference between reversible and irreversible expansion? I know how they are in formulas, (Irreversible-PV, reversible- integral over P in terms of V), but why are they expressed like this? What's the difference? And I would also like to get an exact formula of these two as I can't...
  29. Ghostcrown

    Could the expansion of space tear us apart?

    Is it possible that the forces behind the expansion of space could at some point overcome the fundamental forces holding our molecules together?
  30. M

    Does the expansion of the universe affect gravitational forces?

    I'm a complete and utter layman here, so please forgive any misunderstandings, but I'm just curious about something and wonder if people could say some words on the subject. So as we understand it, the universe is constantly expanding, but expanding at an accelerated rate, so wouldn't this have...
  31. D

    Would Rapid Expansion of a Parallel Universe Affect a Black Hole?

    I have a "What If." question. Suppose a black hole located in a universe encounters a rapid expansion of another universe with the universe that is in close approximation to the black hole. Would the rapidly expanding universe destroy the black hole or would the expanding universe actually...
  32. Suraj M

    Is the Universe Still Expanding Faster Than the Speed of Light?

    So I know that the universe expanded faster than the speed of light. Then it still should be expanding faster than the speed of light,right? Then, how is the light produced during the big bang catching up to us now?? I mean the radio signals and the image of the early universe?
  33. M

    P-adic norm, valuation, and expansion

    In this book I'm working from (P-adic numbers: An introduction by Fernando Gouvea), he gives an explanation of the p-adic expansion of a rational number which I'm pretty sure I understand this, but a bit later he talks about the p-adic absolute value, which from what I understand is the same as...
  34. B

    Designing with Thermal expansion in mind

    Hi, I am trying to design a tubular probe that's made of stainless steel (304), from what I've read it has a Thermal expansion coefficient of around 9.6 x10^-6 in/in/F give or take on the quality. I want to fill this tube halfway with an Epoxy, however from what I've read this epoxy has a...
  35. B

    What Changes During Free Adiabatic Expansion of a Real Gas?

    Homework Statement Which of the following changes during the free adiabatic expansion of a real gas? (I) internal energy (II) temperature (III) pressure Homework Equations PV=nRT; ΔU= q + w The Attempt at a Solution For ideal gases under adiabatic conditions, we know that there is no heat...
  36. Tadhgrrr

    Thermal expansion: the amount of material expanding is "irrelevant"?

    Hello everyone! First time asking a question here, go easy on me! I am a first year Mech-Eng student in Ireland, and I need some guidance from one of the amazing brains here at physicsforums. I am told by my thermofluids lecturer that in thermal expansion, the amount of material expanding is...
  37. R

    Adiabatic irreversible expansion

    This example is taken from the wikipedia page describing irreversible processes. I just want to make sure I understand correctly why the initial state can't be reached anymore. I assume the transitions to be quasi-static, but there is friction between the piston and the cylinder. If so...
  38. AdityaDev

    Calculating Work Done by Expanding Gas in Spherical Bubble

    Homework Statement (1)The gas inside a spherical bubble expands slowly so that its radius is increases from R to 2R. Atmospheric pressure is ##P_0## and surface tension is S. The work done by the gas is ___________ Homework Equations work done against surface tension ##W_t = S.\Delta A## where...
  39. W

    Expansion, Gravity and the Electric Force

    The explanation as to why galaxies like the Milky Way and Andromeda are not expanding away from each other is that they are gravitationally bound, and the expansion at that small scale is not really apparent anyway. My question is purely hypothetical. What if you had a measuring stick that...
  40. H

    Why never any length expansion under Lorentzian Relativity?

    Lorentz believed in the ether, and developed his version of Relativity Theory based on interactions of moving charged particles (electrons, specifically) with the ether. What I don't understand is how one always gets length contraction for movement in an inertial system moving with respect to...
  41. W

    Solve Linear Expansion Problem at 35ºC | AP Physics 2

    A uniform rod of a length of 2.0 m at 5ºC has a coefficient of linear expansion of 5.0 × 10^-4 K^-1. How much longer is it when the temperature is 35ºC? I want to know the procedure to solve this problem This isn't hw, but I'm wondering how to solve it when it's K ^-1 Just trying to get some...
  42. H

    Planar wave expansion cancelling through interference

    Hello everyone! In a hypothetical 3D space, with no boundaries around, homogeneous normal conditions, what would happen to the advancement of a planar wave front produced at t=0 with 2cycles in length, λ=3.5m, moving with vector speed "c-arrow=1i-arrow" if an identical planar wave of 2cycles in...
  43. M

    MHB Taylor Expansion: Wondering Which is Right?

    Hey! :o I want to find the taylor expansion of $f(x, y)=x^2 (3y-2x^2)-y^2 (1-y)^2$ at the point $(0, 1)$ and I got the following: $$f(x, y)=3x^2-(y-1)^2+3x^2 (y-1)-2 (y-1)^3-2x^4-(y-1)^4$$ but a friend of mine got the following result: $$f(x, y)=3x^2-(y-1)^2+3x^2 (y-1)+3x...
  44. Z

    What is the finite expansion of a function means ?

    i know the rules of finite expansion but i just want to know why do we need it and what does it mean ?
  45. julianwitkowski

    Time Dilation Across the Universe: Implications & Expansion

    For two objects at distant parts of the galaxy, because of their relative velocity and the space between them increasing faster than light, does this factor into the time dilation they will experience? I'm tending to think not because the space they are on is relative and it is only space...
  46. L

    Reversible adiabatic expansion proof

    Homework Statement Prove the relationship between the pressure, P, and the temperature, T, for an ideal gas with a reversible adiabatic expansion. Base the proof on the first law of thermodynamics and the ideal gas law. The relationship is: T^(Cp,m/R)/P = constant Where R is the gas constant...
  47. N

    Using Power Series to Evaluate ln and sin at a Given Point

    Homework Statement "Use power series to evaluate the function at the given point" ## ln (x+ \sqrt{1+{x^2}}) - sin x ## at ## x = 0.001 ## Homework Equations Relevant power series: A: ## ln (1+x) = \Big( \sum_{n=0}^\infty\frac{({(-1)^{n+1}}{x^n})}{n} \Big) ## B: ## {(1+x)^p} =...
  48. E

    Work done by product gas in reversible adiabatic expansion

    I am having trouble calculating the work done by a product gas in reversible adiabatic expansion, and in calculating the final temperature. pV gamma = constant, Cv = constant (assume), gamma = cv + nR / Cv. anyone who can help me out?
  49. MexChemE

    Free energy in the free expansion of an ideal gas

    Hello PF! Consider the free expansion of an ideal gas. The process occurs at constant temperature, therefore, ΔU = 0, Q = 0, and W = 0. Suppose we are given the initial and final pressures of the gas, and we calculate ΔG = nRT ln(P2/P1). As P2 < P1, ΔG < 0. This is intuitive, as a free expansion...
  50. M

    Calculating term in Virial Expansion

    Homework Statement ...For each of the temperatures...compute the second term in the virial equation ##B(T)/(V/n)##, for nitrogen at atmospheric pressure. Homework Equations ##PV = nRT(1+\frac{B(T)}{V/n}+\frac{C(T)}{(V/n)^2}+...)## The Attempt at a Solution I'm given a list of temperatures and...
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