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

    I Universe Expansion: Growing or Stretching?

    I apologize if this has been asked before, but I have never seen a satisfactory or straightforward answer. When we say the universe is expanding, do we mean it is "growing" or "stretching"? In other words, if you considered a sheet of graph paper expanding, are we adding more squares or...
  2. T

    Laurent expansion of ##ze^{1/z}##

    Homework Statement Find a Laurent series of ##f(z)=ze^{1/z}## in powers of ##z-1##. Is there an easier way to go about this as this is not a typical expansion I see on textbooks. It seems that my incomplete solution is too complicated. Please help, exam is in two days and I am working on past...
  3. N

    A Partial Fraction Expansion

    Hi, I would like to expand the following expression: 1/[((a+s)*(1+b/s)^m)], where a, b, and s are real nonnegative values and m is an arbitrary positive integer. Particularly, according to partial fraction expansion, it becomes: Sum[A_j/[(1+b/s)^j],{j,1,m}]+B/(a+s). I look for a closed-form...
  4. binbagsss

    Statistical Mechanics- moments/cumulants, log expansion

    Homework Statement Using log taylor expansion to express cumulants in terms of moments I have worked through the expansion- ##log(1+\epsilon)= ...## see thumbnail- and that's ok; my question is why does the expansion hold, i.e. all i can see is it must be that ##k## is small- how is this...
  5. E

    B Accelerating Expansion of Cosmos: Measured in Multiple Directions?

    Does anyone know if the accelerating expansion of the universe was measured in more than one direction? Unlike the expansion having no obvious center, it seems like the accelerating expansion would have to point to a “center”. Our galaxy, for example, cannot be accelerating away from a...
  6. R

    I Accelerating universe explained by constant expansion?

    Why is the accelerating expansion of the universe not explained simply by the perspective of acceleration caused by a constant (non accelerating) universal expansion? Let's take two particles (X,Y) in a 1d expanding universe where it expands universally by 1 unit per per unit time. O represents...
  7. P

    Radius of Convergence and Power Series Expansion Around Multiple Values

    Homework Statement Suppose we are given the power series expansion ##f(x) = -\sum_{n=1}^{\infty} \frac{x^{n}}{n} ## which converges for |z|<1. What is the radius of convergence? Sum this serie and derive a power series expansion for the resulting function around -1/2, 1/2, 3/4 and 2. The...
  8. J

    Partial Fraction Expansion - Repeated Roots Case

    Homework Statement Find Partial Fraction Expansion 10/[s (s+2)(s+3)^2] Homework EquationsThe Attempt at a Solution 10/[s (s+2)(s+3)^2] = A/s + B/(s+2) + C/(s+3)^2 + D/(s+3) A = 10/[(s+2)(s+3)^2], s approaches 0 = 10/(2*3^2) = 5/9 B = 10/[s (s+3)^2], s approaches -2 = 10/(-2) = -5 C =...
  9. R

    Find the coefficient from the expansion (Explanation request

    Homework Statement Coefficient of xy(z^-2) in (x-2y+3(z^-1))^4 Homework EquationsThe Attempt at a Solution [/B] I was wondering if anyone could give me an explanation for my answer? The coeffecient of xy(z^-2) does not = 4 where I would be able to use the multinomial theorem. So since I...
  10. benorin

    B The geometry of the expansion of space

    I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose...
  11. N

    I Length Expansion Opposite Direction: SR Simultaneity Explained

    SR says that there is length contraction in the direction of movement. This works nicely for light going from the back of the ship to the front. From my perspective, the ship is moving away but that is offset by the ship's contraction. But things get tricky for light going from the front of the...
  12. Inani Schroedinger

    I Is the expansion actually accelerating? Or does it just appear so?

    I pulled this quote from an article on the Hubble Constant: "...for example, if the Hubble Constant was determined to be 50 km/s/Mpc, a galaxy at 10 Mpc, would have a redshift corresponding to a radial velocity of 500 km/s." In this illustration provided from the article, if this was the...
  13. U

    A Taylor expansion for a nonlinear system and Picard Iterations

    Hello guys I struggle since yesterday with the following problem I am reading the book "Elements of applied bifurcation theory" by Kuznetsov . At one point he has the following Taylor expansion of a nonlinear system with respect to x=0 where ##x\in \mathbb(R)^n## $$\dot{x} = f(x) = \Lambda x +...
  14. K

    I Interstellar Travel vs Universe Expansion: Is Andromeda Reachable?

    I read in a so called sci-fi website from my country that as the universe is expanding we may not be able to get to certain galaxies in a possible interstellar travel. That information seems ok for me. But then there was a comment by a reader concluding from the website post that there is coming...
  15. kolleamm

    B The accelerating expansion of the universe

    Just a thought I had today. I read an article that mentioned how the universe is expanding faster and faster and how dark energy may be the cause for this, but I wondered, what if the accelerating expansion of the universe is not caused by dark energy but simply by the gravitational attraction...
  16. W

    I Understanding Confusing Expansion: Taylor Series Expansion

    I came across the following working in my notes and would like some help understanding how the step was done. Many thanks in advance! The following is the working, and we assume that ##\beta## is small $$\frac{1}{1+ \beta \hbar \omega /2 + (7/12)(\beta \hbar \omega)^2 +...} \approx 1 - (\beta...
  17. G

    B Is the cosmic expansion uniform everywhere?

    I seek a little help in understanding why we can see so far into the past to be able to view events where the light from these events should have long ago overtaken wherever the masses ended up. I get it that there was a considerable time during which the limits of the space expansion exceeded...
  18. M

    I Will Space Expansion Lead to the Formation of Black Holes and Neutron Stars?

    1) space is expanding at an increasing rate, therefore things are getting farther from each other and therefore increasing in velocity. 2) the faster an object moves relative to another, the more mass it has 3) supermassive objects can turn into neutron stars, black holes, etc. Therefore, will...
  19. D

    I Finding expansion coefficient of a 3-d Gaussian wave packet

    I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...
  20. A

    Relation Between Ma and Re for Isentropic Expansion

    Homework Statement Consider the isentropic expansion of air from a fixed given reservoir (i.e. total pressure and temperature). Investigate the behaviour of the value of the Reynolds number of the flow, as a function of the Mach Number M of the expanded flow. For small values of M, the...
  21. A

    MHB Exploring the Bessel Function Expansion

    Bessel function using g(x,t)=g(u+v,t)=g(u,t)g(v,t) to show that J_{0}(u+v)=J_{0}(u)J_{0}(v)+2\sum_{s=1}^{\infty}J_{s}(u)J_{-s}(v) ___________________________________________________________________________________________ my solution g(u+v,t)=e^{\frac{u+v}{2}(t-\frac{1}{t})}...
  22. l0st

    I Gravitational Waves Cause Uniform Space Expansion: Exploring MNRAS Papers

    I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the...
  23. T

    I Why does the expanding universe redshift light?

    How does the expansion of space cause light to lose energy?
  24. Deepblu

    B How do we know that the universe is still expanding

    This idea has always bugged me: If we are looking at the past when observing the redshift of far away galaxies (ex: 10 billions light years).. then how can we tell that the universe at the present time is still expanding at same rate, deaccelerated, or stopped expanding?
  25. redtree

    I Redshift and the Friedmann metric

    My discussion of the Friedmann metric comes from the derivation presented in section 4.2.1 of the reference: https://www1.maths.leeds.ac.uk/~serguei/teaching/cosmology.pdf I have a couple of simple questions on the derivation. The are placed at points during the derivation.I note the...
  26. baldbrain

    Iron Ring Expansion: Solve for Δθ to Find Temp Increase

    Homework Statement An iron ring of radius 2.1 m is to be fitted on the rim of a wheel of radius 2.121 m. The coefficient of volume expansion for iron is 3.6 x 10-5 K-1. By how much should the temperature of the ring be increased? (a) 532 °C (b) 833 °C (c) 278 °C (d) 378 °C Homework Equations...
  27. chwala

    Finding the convergence of a binomial expansion

    Homework Statement Expand ##(1+3x-4x^2)^{0.5}/(1-2x)^2## find its convergence valueHomework EquationsThe Attempt at a Solution on expansion ##(1+3/2x-3.125x^2+4.6875x^3+...)(1+4x+12x^2+32x^3+...)## ##1+5.5x+14.875x^2+42.1875x^3+... ## how do i prove for convergence here?
  28. WeiShan Ng

    I How Does Angular Diameter Distance Apply to the Last Scattering Surface?

    The definition of the angular diameter distance is the ratio of an object's physical transverse size to its angular size. However when I was reading my textbook, *Astrophysics in a Nutshell by Dan Maoz pp.220-221*, I am having some trouble trying to understand the notion of **angular diameter...
  29. G

    Volume ratio in an adiabatic gas expansion

    Homework Statement Consider a perfect monoatomic gas at pressure $p_i$ 1.2 atm and temperature $T_i$ 300K, that is in equilibrium inside a cylinder having a volume $V_i=1L$ and which piston has a mass of 1kg and is at an height of 50 cm. Admit that a mass M=3.13kg is over the piston. When that...
  30. M

    Are flow work and work done during isobaric expansion similar?

    In case of isobaric expansion, the system expands at constant pressure(the external pressure i.e. the resistance is constant.).In case of flow work, the fluid trying to exit the control volume, pushes against the pressure at the exit of the control volume or when entering the control volume, the...
  31. M

    Isothermal Expansion w/ Equal Pressures

    In an isothermal expansion of an ideal gas, can the piston be made to expand isothermally if the initial system pressure is equal to the initial surrounding pressure?(In most of the books and video lectures whenever they explain isothermal expansion, they assume initial system pressure to be...
  32. M

    Why pressure decreases during isothermal expansion?

    Initially, the pressure of the gas inside the cylinder is higher than the atmospheric pressure and the piston is held in the contracted position by some means.When the piston is released, it expands and the pressure and temperature of the system decreases but the volume increases.In order to...
  33. M

    I Regarding Joule's gas expansion experiment

    Hi, Joule's original gas expansion experiment is often presented like in the following link: http://demonstrations.wolfram.com/JouleExperimentOnFreeExpansion/ The apparent lack of temperature change in this experiment is often used in textbooks to demonstrate that the energy of an ideal gas is...
  34. R

    What is the Taylor expansion of x/sin(ax)?

    Hey everyone 1. Homework Statement I want to compute the Taylor expansion (the first four terms) of $$f(x) =x/sin(ax)$$ around $$x_0 = 0$$. I am working in the space of complex numbers here. Homework Equations function: $$f(x) = \frac{x}{\sin (ax)}$$ Taylor expansion: $$ f(x) = \sum...
  35. J

    Coefficient of volume expansion of gas

    Homework Statement Homework EquationsThe Attempt at a Solution Coefficient of volume expansion γ = ∆V/V∆T VT2 = constant Differentiating we get , T2∆V + 2VT∆T = 0 ∆V/V∆T = -2/T So , option 2) looks right . Is that correct ? How do I interpret the answer ? Does that mean the...
  36. platosuniverse

    B Doesn't there have to be more than one observable universe?

    I was just curious because if space can expand faster than light, doesn't that mean there will be a lot of space that we just can't see? Do objects just vanish because we can't see them? For instance, if a hypothetical alien lived in MACS0647-JD galaxy which is 13.3 billion light years away...
  37. Hamza Abbasi

    Strain produced in a rod after expansion

    Homework Statement A rod of length ##L_o## is kept on a friction-less surface. The coefficient of linear expansion for the material of the rod is ##\alpha##. The the temperature of the rod is increased by ##\Delta T## the strain developed in the rod will be? Homework Equations $$ \Delta L=...
  38. Nabin kalauni

    B What does coefficient of increase of physical quantity mean?

    I am extremely confused by the use of the term coefficient of increase of something. For example , if it is stated that the index of refraction varies linearly with a coefficient of 2.5×10^-5, how is this coefficient defined? Is it simply the slope of the line plotted with index of refraction on...
  39. E

    I Question about accelerating expansion

    Question about accelerating expansion Why do I see everything backwards? Here is a paragraph from Bernard Schutz’s excellent book on General Relativity, p. 352: (referring to the famous plot from the High-Z Supernova Search Team: Riess, et al, 1998) The top diagram shows the flux (magnitude)...
  40. ScottHendo

    Thermodynamics - Enthelpy change in adiabatic expansion

    Homework Statement Adiabatic expansion of an ideal gas is carried out in a steady flow process. The initial pressure of the gas is 2.5 bar. The volume is expanded from 1.2m3 to 3.8m3. Heat capacity ratio (γ) = 1.42. Calculate enthalpy change of the process. Homework Equations PV = nRT W = ∫...
  41. C

    MATLAB Karhunen Loeve Expansion in Matlab

    Hello everyone. I am trying to generate the KL expansion of a stochastic process. I use a Monte Carlo sampling method to generate the process, which involves two random variables and I compare it with it's theoretical mean for 50 values of time and they look quite similar. Then, I calculate the...
  42. WeiShan Ng

    Deriving magnetic dipole moment from multipole expansion

    Homework Statement This is from Griffith's Introduction to Electrodynamics, where the book is deriving the magnetic dipole moment from multipole expansion of the vector potential The vector potential of a current loop can be written as $$\mathbf{A(r)}=\frac{\mu_0 I}{4\pi} \left[ \frac{1}{r}...
  43. D

    B Unraveling the Mystery of Universe Expansion: Exploring External Energy Sources

    So I was doing some studying and got a question on why the rate of expansion of the universe was increasing, and it got me thinking. Newton's first law states that an object in motion will remain in motion with a constant speed unless an external force acts upon it. If the expansion of the...
  44. alantheastronomer

    A Gravitational Waves: Expansion of Spacetime?

    Gravitational waves are quadrupoles, they bend and stretch spacetime. Does the expansion of spacetime due to gravitational waves exceed flat (Minkowski) spacetime or is flat spacetime it's limit?
  45. C

    A How to relate the expansion term to Feynman diagrams

    I learn quantum field theory using the book of " quantum field theory in a nutshell" by A. Zee. But I am confuse when I read the content about the "baby problem" at the beginning of "1.7 Feynman Diagrams". In that section, author get the term of order λ and [J][/4] by -(λ/4!)[(d/dJ)][/4]...
  46. C

    I The deviation of Universe expansion from general relativity

    What is the deviation in the expansion of the universe exactly quantified, when I would assume general relativity and project it backwards? As a statistician I am asking for data, for either the backwards projected general relativity case and either the real expansion case, as it is...
  47. Bandersnatch

    I Are there any local effects of Einstein-de Sitter expansion?

    The question is whether or not expansion in flat, matter-only universes (no lambda) has any effect whatsoever - no matter how negligible - on dynamics of small-scale systems. Context: It's a variation on the 'is Brooklyn expanding?' type of questions. My understanding has always been that...
  48. K

    B Distance Expansion When Moving Away from an Object?

    In a physics video on YouTube it's told that moving away from an object causes eextension of the length. (Link: from 6:00, but video is Norwegian) Imagine: From planet B to planet C, the distance is 20 light years. And from planet A to planet B the distance is 20 light years. We are on...
  49. B

    What is the correct solution for the temperature expansion problem?

    Homework Statement A steel container is filled with alcohol. For how much kelvins we have to raise the temperature for the pressure to be raised by 6 bar? Compressibility of alcohol is \kappa=1.15 \cdot 10^{-4} bar^{-1} temperature coefficient of volume expansion of alcohol is \beta_a=...
  50. F

    Pipe Expansion Loops: Benefits, Features & Usage

    Pipe loops are used to accommodate thermal expansion. I have seen many types and lengths but here is one example: https://www.engineeringtoolbox.com/steel-pipe-expansion-loop-d_1069.html I am a little unclear on why they can work. With any thermal expansion the stresses on the elbow joints...
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