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. 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] \\...
  2. G

    Plane wave expansion of massive vector boson

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  3. 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!
  4. H

    Beginning of accelerating expansion

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  5. theOrange

    Load carrying expansion joints

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

    Thermal Expansion of a shrink-fit collar

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  7. T

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

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  8. K

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

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  9. C

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  10. U

    Find the expansion of this term

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  11. C

    Intuition on the Friedman equation: curvature and expansion

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  12. S

    Start of expansion of universe

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  13. J

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

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  14. L

    Why is the Universe Expanding and Not Contracting?

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  15. P

    Gas Expansion in insulated cylinder (piston & Diaphragm)

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  16. J

    Finding coefficient of thermal expansion

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  17. N

    MHB Eigenfunction expansion with chebyshev

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  18. 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 (...
  19. I

    Virial Expansion of Van Der Waals Equation

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  20. W

    Thermodynamics problem for gas expansion at constant-volume

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  21. T

    Ideal gas expansion between two tanks (Thermodynamics)

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  22. H

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  23. I

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

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  24. F

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  25. S

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  26. M

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  27. V

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  28. S

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  29. I

    Partial Expansion in high pressure Turbine in a Reheat Rankine cycle

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  30. 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?
  31. T

    Expansion of the universe | Potential Effects on Energy / Matter

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  32. 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.
  33. 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...
  34. 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?
  35. 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}...
  36. W

    Asymptotic expansion on 3 nonlinear ordinary differential equations

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  37. WannabeNewton

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  38. C

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  39. Greg Bernhardt

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  40. 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 +...
  41. TumblingDice

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    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...
  42. 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 -...
  43. C

    Expansion of Space vs Velocity in Space

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  44. A

    Coefficient of x^r in Expansion of (1+x)(1-x)^n

    I am puzzled by the following example of the application of binomial expansion from Bostock and Chandler's book Pure Mathematics: If n is a positive integer find the coefficient of xr in the expansion of (1+x)(1-x)n as a series of ascending powers of x. (1+x)(1-x)^{n} \equiv (1-x)^{n} +...
  45. N

    Does the bond between atoms affect Thermal Expansion?

    Homework Statement From a journal I read that the cobalt-based perovskite cathode usually has better ionic and electrical conduction but higher TEC compare to Maganite-based perovskite cathode. Because of the Co-O bond is weaker than Mn-O bond. e.g. Cobalt-based perovskite cathode...
  46. J

    On general expansion of cos nΘ

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  47. B

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  48. T

    Power Expansion (Complex variables)

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  49. @

    Was the expansion of the universe always greater than c?

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  50. T

    Expansion of a local dissipation function

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