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. I

    Relativistic mechanics Taylor expansion

    Homework Statement For a particle traveling near the speed of light, find the first non-vanishing term in the expansion of the relative difference between the speed of the particle and the speed of light, (c-v)/c, in the limit of very large momentum p>>mc. Hint: Use (mc/p) as a small parameter...
  2. R

    Sinking instead of expanding universe?

    We all know the concept of the universe expanding. Would it be possible that the universe is not expanding at all, but the spacetime between objects is increasing? My question comes from the idea that spacetime is changed due to the presence of gravitational objects and the idea that gravity is...
  3. E

    Multipole expansion - small problem

    Homework Statement Jackson 4.7 Given a localized charge distribution: \rho(r)=\frac{1}{64\pi}r^{2} e^{-r} sin^{2}\theta make the multipole expansion of the potential due to this charge distribution and determine all nonvanishing moments. Write down the potential at large distances as a...
  4. Flutterguy123

    What is the rate of gas expansion in a vacuum?

    Say that there's a large metal box with nothing but a vacuum inside of it, except for a small bag of compressed gas at the center. If the bag were to suddenly pop, is there a specific rate that this gas would accelerate when expanding to meet the space of the container? I think that it might...
  5. skate_nerd

    MHB Does this problem warrant a taylor expansion? (solid state physics)

    The whole problem I'm doing here is not even really relevant, so I won't go too much into it...I'm told to find an atomic form factor given some certain conditions, and I do a big gross integral and got this: $$f=(\frac{4}{4+(a_oG)^2})^2$$ where \(a_o\) is the Bohr radius and \(G\) is the...
  6. K

    Solving expansion rate for a variant of the Friedmann equation

    Homework Statement For the equation H^2 = \frac{8 \pi G \rho_m}{3} + \frac{H}{r_c} how do I find the value of H for scale factor a \rightarrow \infty , and show that H acts as though dominated by \Lambda (cosmological constant) ? Homework Equations \rho_m \propto \frac{1}{a^3} H > 0...
  7. Z

    Understanding Expansion of Space

    So what I don't get about the expansion of space, and what I'm assuming one of you can explain to me, is that it seems like if space were expanding, how would we have any way of noticing it? It seems like as the distances between particles expands, so must the size of the particles themselves...
  8. A

    Why D? Exploring Isothermal Expansion

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  9. A

    Prove: Binomial Expansion for e^{2x}-1/e^{2x}+1 up to x^5

    Homework Statement Prove that, if x is so small that x^6 and higher powers of x may be neglected, then \frac{e^{2x}-1}{e^{2x}+1}\approx x-\frac{x^3}{3}+\frac{2x^5}{15} Homework EquationsThe Attempt at a Solution [/B] \\...
  10. G

    Plane wave expansion of massive vector boson

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  11. P

    The temp. dependent Specific heat and expansion coefficient of Cobalt?

    Hey. I am writing my master thesis, and I really need to find the temperature dependent heat capacity and expansion coffient for Cobalt. I have tried searching the internet, whitout luck. Please, can anybody help me. It is really important!
  12. H

    Beginning of accelerating expansion

    I've been trying to find the latest, best guess, as to how long ago the universe's expansion began to accelerate (post-inflation). I've seen various estimates on websites from 5 billion to 8 billion years ago. Is there any kind of consensus in the community that studies these things as to a...
  13. theOrange

    Can regular maintenance prevent all failures in bridges and machines?

    Are there any expansion joints (for example between two beams) which can carry a shear force?
  14. A

    Thermal Expansion of a shrink-fit collar

    Looking for some information on how a shrink fit collar actually works. I get the basic principle that you heat it, it expands, fit the collar, let it cool and it contracts and grips as a collar. However, if you heat a material am I right in saying that it expands in all direction. If this is...
  15. T

    Binomial Expansion: Coefficient of x^3 in (2/x-3x^4)^12

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  16. K

    Weinberg 3.4 -- Derive the perturbation expansion....

    Homework Statement Basically I wanted to see if anyone would be willing to give me the solution to the 4th problem of the Weinberg textbook on quantum field theory. The exact question in the book is "Derive the perturbation expansion (3.5.8) directly from the expansion (3.5.3) of old-fashioned...
  17. C

    Expansion of series and possible induction

    Homework Statement Consider the infinite series $$\frac{x}{e^x - 1} = A_o + A_1 x + \frac{A_2}{2!}x^2 + ... + \frac{A_n}{n!}x^n + ...$$ Determine that ##1 = A_o,\,\,\,\,\,0 = A_o/2! + A_1,\,\,\,\,\,0 = A_o/3! + A_1/2! + A_2/2!##. Show that for ##n > 1##, one can write the relations as $$(A+1)^n...
  18. U

    Find the expansion of this term

    Homework Statement IF e^{m \arctan x}=a_0 + a_1x + a_2x^2 + a_3x^3...+a_nx^n+... prove that (n+1)a_{n+1} + (n-1)a_{n-1}=ma_n and hence obtain the expansion of e^{m \arctan x} . Homework Equations The Attempt at a Solution $$e^{m \arctan x} = 1+m \arctan x + (m \arctan x)^2/2! + (m...
  19. C

    Intuition on the Friedman equation: curvature and expansion

    The Friedmann equation states that $$(\frac{\dot a}{a}) = \frac{8\pi G}{3} \dot \rho + \frac{1}3 \Lambda - \frac{K}{a^2},$$ where ##a, \rho, \Lambda, K## respectively denotes the scale factor, matter density, cosmological constant and curvature. Now, I'm trying to get at an intuition on...
  20. S

    When Was the Universe's Expansion Rate Zero?

    I have been wondering for a few years if the current equations for the expansion of the universe have ever been used to extrapolate back in time, to determine how many years ago, the rate of expansion was zero. I believe this amount of time will not agree with the accepted age of the universe...
  21. J

    Fluids with high expansion ratios that do not leave the liquid state

    Hey guys, I've been doing a lot of research looking for a fluid that has a high expansion ratio that does not leave the liquid state. the idea is that the fluid could either: - using heat will expand and contract using hot and cold cycles - using electricity (not necessarily needing...
  22. L

    Why is the Universe Expanding and Not Contracting?

    Can someone please explain to me why the universe must be expanding and not contracting? Here is my take on this. The Doppler Effect tells us that we are moving faster than objects. "Behind" us, and objects "ahead" of us are moving faster still. Hence the inference of expansion. But , if...
  23. P

    Gas Expansion in insulated cylinder (piston & Diaphragm)

    I attached an image of two expansion cases I am analyzing. Both cases involve an insulated cylinder that is divided by a separating element (diaphragm for case A and piston for B). The portion on the right is evacuated. The left contains a calorically perfect gas with an initial pressure and...
  24. J

    Finding coefficient of thermal expansion

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  25. N

    MHB Eigenfunction expansion with chebyshev

    I am absolutely dying with this question. Ok so referring to the attached image; we can re-iterate the given equation in SL-Form. so $(1-x^2)u'' - xu' + 2u =0 $ divide everything by $\sqrt{1-x^2}$ so we get $\sqrt{1-x^2}u'' - \frac{x}{\sqrt{1-x^2}} u' + \frac{2}{\sqrt{1-x^2}}u=0$ which...
  26. Domenico94

    Why is the universe expanding at an accelerating rate?

    Hi everyone. I'm new to this forum...I just want to make it clear that I'm an engineering student, thus I don't want to look conceited with what I'm going to say. Some day ago, I was watching a documentary talking about the universe ( its expansion in particular), in which it was shown that (...
  27. I

    Virial Expansion of Van Der Waals Equation

    Homework Statement If the compressability factor is given at a certain temperature as a function of pressure: Z(T) = 1+αP+βP2 find α and β in the form α(a, b, T) and β(a, b, T) where a and b are the van der waals coefficients. Homework Equations nRT=(P+a(n/V)2))(V-nb) Z=PV/nRT The Attempt...
  28. W

    Thermodynamics problem for gas expansion at constant-volume

    Homework Statement This is a paraphrase, since this is only part of a 3 part question. A sample of 1.00 mol perfect gas molecules with C_{p,m}=7/2*R and initial pressure of 1.00 atm undegoes constant-volume heating to twice its initial pressure. Find q, w, ΔU, and ΔH.Homework Equations PV=nRT...
  29. T

    Ideal gas expansion between two tanks (Thermodynamics)

    Homework Statement Two interconnected tanks are of equal volume. One is filled with methane at 500bar and 293K, the other is initially evacuated. A valve connecting the two tanks is opened only long enough to allow the pressures to equilibrate. If there is no heat transfer between the gas and...
  30. H

    How do I calculate adiabatic work done by a gas during expansion?

    Homework Statement Hi, I did a lab experiment where I took a 5L vessel made of some material that isolates gas inside and thus behaves like an isolated system (adiabatic). I then pumped gas from ~90kPa to up to 150 kPa... recorded the temperature, then let the gas 'expand' by opening the...
  31. I

    Light propagates faster than the rate of expansion of the universe?

    I know the universe doesn't expand at a speed but rather a rate over distance but if we take two objects on opposite sides of the observable universe, would they be moving away from each other at a greater rate than light? IE if object A was a star and object B was a planet, would the light...
  32. F

    Lowering temparture of a gas due to slow expansion

    Hi people, I just found out that the famous Feynman Lectures on Physics are now online, so I'm going through them just for fun (I took Physics in College a long long time ago, but was too much content with too little time to actually understand it for real, so here I'm again learning it)...
  33. S

    Universe Expansion: Is Merging Possible?

    Is it possible that our universe is just one of more universes and that our universe just appears to be expanding because we are actually merging with another universe? Just wondering if it would be a plausible explanation. Maybe the pull from the other universe against the pull from ours...
  34. M

    Expansion by doppler (red) shift

    Hello all, so I've always wondered about the expansion of the universe as indicated by the observed doppler (red) shift... i get the observed spectrum change and how this can be credited to the stretching of electromagnetic waves... what doesn't make sense to me is that if this is due to a...
  35. V

    Expansion of scalar function times laplace's equation

    Apparently, f \nabla^2 f = \nabla \cdot f \nabla f - \nabla f \cdot \nabla f where f is a scalar function. Can someone please show me why this is step by step. Feel free to use suffix notation. Thanks in advance.
  36. S

    Thermal expansion of a copper pipe

    Homework Statement Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 63.1 m of copper pipe whose inside radius is 7.69 x 10^-3 m. When the water and pipe are heated...
  37. I

    Partial Expansion in high pressure Turbine in a Reheat Rankine cycle

    Please help me with this, In Reheat Rankine cycle, we first Expand the steam partially in a high pressure turbine and then reheat it again . How is this partial expansion in high pressure turbine done ? in the sense, what is the procedure followed to have only partial expansion of steam...
  38. S

    Multiplying Christoffel Symbols w/o Overloading Indices

    This expression: \Gammaavc\Gammacab Can someone please show me how to multiply the two Christoffel symbol formulas for these Christoffel symbols without overloading any indices?
  39. T

    Expansion of the universe | Potential Effects on Energy / Matter

    I have been thinking for the past couple months on how the expansion of the universe effects the matter and energy within it. Please read every line, skipping any part of this thread will lead to confusion. Hopefully someone can shed some light on this amazing new question of universal expansion...
  40. M

    Low Thermal Expansion Coefficient Glass Tube

    Hi All, I would like to ask if what supplier's fabricate Low Coefficient of Thermal Expansion (CTE) glass tubing for Fiber Optics application. or What type of glass do we need in Low CTE? It will serve as the packaging for DWDM components. Hoping for your response. Thank you.
  41. T

    How can a Fourier expansion contain all the same info as original f'n?

    We know that a function f(x) over an interval [a, b] can be written as an infinite weighted sum over some set of basis functions for that interval, e.g. sines and cosines: f(x) = \alpha_0 + \sum_{k=1}^\infty \alpha_k\cos kx + \beta_k\sin kx. Hence, I could provide you either with the function...
  42. I

    MHB Taylor Series Expansion and Radius of Convergence for $f(x)=x^4-3x^2+1$

    find the taylor series for $f(x)=x^4-3x^2+1$ centered at $a=1$. assume that f has a power series expansion. also find the associated radius of convergence. i found the taylor series. its $-1-2(x-1)+3(x-1)^2+4(x-1)3+(x-1)^4$ but how do i find the radius of convergence?
  43. R

    MHB Asymptotic expansion on 3 nonlinear ordinary differential equations

    The 3 nonlinear differential equations are as follows \begin{equation} \epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber \end{equation} \begin{equation} \frac{ds}{dt}= \lambda_b P_C \ \epsilon \ c (1-s)- \lambda_r (1-q) \ s, \nonumber \end{equation}...
  44. W

    Asymptotic expansion on 3 nonlinear ordinary differential equations

    The 3 nonlinear differential equations are as follows \begin{equation} \epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber \end{equation} \begin{equation} \frac{ds}{dt}= \lambda_b P_C \ \epsilon \ c (1-s)- \lambda_r (1-q) \ s, \nonumber \end{equation}...
  45. WannabeNewton

    Series expansion tetrad Fermi coordinates

    Hi all. I'm working on a project that requires me to perform calculations in Fermi normal coordinates to certain orders, mostly 2nd order in the distance along the central worldline orthogonal space-like geodesics. In particular I need a rotating tetrad propagated along the central worldline...
  46. C

    Series expansion of the signum function of sine

    Hi, I just read a physics paper and there it expands signum of a sine function as below: sgn(sin(wt))=(4/pi)*{sin(wt)+(1/3)*sin(3wt)+(1/5)*sin(5wt)+...} How can we expand sgn(sin(wt)) like this? Thanks.
  47. Greg Bernhardt

    What Is the Expansion Postulate in Quantum Mechanics?

    Definition/Summary The Expansion Postulate is a fundamental postulate in the formalism of quantum mechanics which states that any wavefunction that describes a possible state of a quantum system can be written as a linear combination of the eigenfunctions of a linear hermitian operator...
  48. A

    Binomial expansion, general coefficient

    Homework Statement Find the coefficient of x^n in the expansion of each of the following functions as a series of ascending powers of x. \frac{1}{(1+2x)(3-x)} Homework Equations The Attempt at a Solution (1+2x)^{-1} = 1 + (-1)2x + \frac{(-1)(-2)}{2!}(2x)^2 +...
  49. TumblingDice

    Expansion, redshift, and conservation of energy

    I've often read posts where the conservation of energy is questioned regarding redshift due to expansion. The question arises because the energy level of photons is directly related to the light's frequency, and this alludes to photons "losing" energy as the frequency lowers. The reasoning I've...
  50. A

    Binomial expansion of (1+(1/x))^(-1)

    Expand the following functions as a series of ascending powers of x up to and including the term x^3. In each case give the range of values of x for which the expansion is valid. (1+(1/x))^(-1) The Attempt at a Solution 1 + (-1)(1/x) + (-1)(-2)(1/x^2)/2 + (-1)(-2)(-3)(1/x^3)/3! = 1 -...
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