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. S

    New volume of balloon after adiabatic expansion

    Result My attempt
  2. Ahmed1029

    I Exact electrostatic potential of a pure dipole using multipole expansion

    If I have a physical dipole with dipole moment p. Now, this formula for potential (V) is a good approximation when r is much larger than both r1 and r2 in the picture below. It's however said that for a pure dipole for which the separation between charges goes to zero and q goes to infinity, the...
  3. U

    Adiabatic expansion with temperature-dependent gamma

    The statement does not say whether the process is reversible or not, but I suppose the only way to solve the problem is by thinking it actually is. I tried using the formula for reversible adiabatic processes, i.e. PVγ = constant. First, I calculated the initial volume with the ideal gas law...
  4. M

    I Universe Expansion: Does Less Dense Mean Boundaries?

    If the universe is "expanding", does that mean less dense, or does that mean there are measurable boundaries? With very far away galaxies that stay "alive" for a "short" time, is most of the very distant observable-from-earth universes now gone?
  5. A

    Problem with a taylor serie expansion

    Greetings https://www.physicsforums.com/attachments/295843 I really don´t agree with the solution https://www.physicsforums.com/attachments/295846 as I calculated fxy I got fxy=xyexy f(0,1)=0 so x(y-1) should not appear in the solution am I wrong? thank you!
  6. M

    I Equivalence of Universe Accelerating Expansion?

    Without suggesting that there actually is a massive spherical shell enclosing the universe, I am trying to explore whether the observed expansion of the universe would be the same if there was a spherical shell with a diameter greater than the universe, with some arbitrary mass producing a...
  7. Cerenkov

    I Edwin Hubble and the Evidence for Universe Expansion

    [Moderator's note: Spin off from previous thread due to topic change.] It's my understanding that Edwin Hubble used the Hooker telescope to measure the red shift of galaxies only within the Local Group of galaxies to determine that the universe was expanding. As we see here...
  8. R

    B Earth's orbit and the expansion of the Universe

    Does the Earth's orbit get very slightly larger over long periods of time due to the expansion of the universe? If so does it stay at the slightly larger distance or somehow does the energy to go back to the earlier orbit go somewhere else and if so where? If the orbit does not get slightly...
  9. moriah

    What is the Source of Strange Sewer-Like Fumes Causing Reactions?

    I am in the need of airtight materials. Naturally, metal came to my mind. Metal is used in jar tops to create “airtight” seals. However, as I contemplated how the tops must expand slightly as they are screwed down towards the glass part of the jars, I wondered if this expansion compromises...
  10. J

    B Accelerating expansion of the Universe

    Will the universe keep expanding faster and faster for all eternity or is there a limit to how fast the expansion will get?
  11. B

    B Loschmidt's paradox and free gas expansion

    Following up on a previous discussion: https://www.physicsforums.com/threads/conservation-of-momentum-in-a-closed-system.1009693/post-6570341 An uncontained system of particles interacting only by elastic collision is the same as a gas undergoing free expansion. If, for simplicity, the...
  12. LCSphysicist

    How to find the coefficients of this expansion?

    I have solved a differential equation whose solutions is $$u = B + \sum_{n=1} C_{n }e^{-\lambda_{n}² q² t} J_{0}(\lambda_{n}r)$$ Where ##(\lambda_{n}r)## is such that ##J_{0}'(\lambda_{n}a) = 0##. So i should now try to satisfy the condition that, at t=0, u = ##f(r)##. The problem is that i...
  13. RogerWaters

    B What is the relationship between expansion and curvature?

    Physics novice here reading pop sci cosmology. Please bear with me. Premise 1: Whether or not expansion is slowing down or speeding up depends on a battle between two phenomena: the attractive gravitational pull of matter and the repulsive gravitational push of dark energy. What counts in this...
  14. A

    Which Little "o" to use for Maclaurin expansion?

    I have calculated it and got the answer but for the first equation with the division the little o is (x^3), I believe and for the equation being multiplied by sin, little o is (x^4) For my answer do I add little o(x^4)?
  15. BWV

    B Observers sending signals to measure expansion

    Googling you find a current expansion rate of ~70 km/s or 0.0002C but of course we don't observe this with objects in the solar system as local gravity prevents this expansion - otherwise a distances would increase by a light second roughly every 71 minutes (maybe I’m missing some here...
  16. Z

    How to choose the correct function to use for a Taylor expansion?

    Consider two different Taylor expansions. First, let ##f_1(s)=(1+s)^{1/2}## $$f_1'(s)=-\frac{1}{2(1+s^{3/2})}$$ Near ##s=0##, we have the first order Taylor expansion $$f_1(s) \approx 1 - \frac{s}{2}$$ Now consider a different choice for ##f(s)## $$f_2(s)=(1+s^2)^{1/2}$$...
  17. cianfa72

    I About Reversible vs Irreversible Gas Compression and Expansion Work

    Hi, reading the interesting Reversible vs Irreversible Gas Compression and Expansion Work insight by @Chestermiller I would like to ask for clarification on some points. In the second bullet at the beginning my understanding is as follows: consider an ideal gas contained in a cylinder...
  18. Sunny007

    I Thermal Expansion of A Square Shaped Object

    Suppose a square shaped object has an initial length of L1 and final length (after thermal expansion) of L2. Initial temperature is T1 and final temperature is T2. Suppose it has an area of A. So initial area is A1 and final area is A2 (after thermal expansion). Here A1 = (L1)^2 and A2 = (L2)^2...
  19. S

    B Expansion of space affecting photon's energy

    On a long trip the photon goes, but it occupies a wavelength of space at any particular time. If the space between start and finish (inspection) is expanding all the way all the journey time, then most of the expansion has no effect on the photon. Like eg second tenth is section currently passed...
  20. C

    Can I improve the sinc interpolation?

    Hello everyone. I am working with mathematica, where I have developed a two-dimensional shannon interplation, just as can be seen in the slides 15 to 18 of this presentation. The code is as follows: savedX = Table[XposX = mat[[All, 1]]; YposX = mat[[All, 2]]; windXVal = mat[[All, i]]...
  21. A

    I How do gravitational waves differ from the expansion of the Universe?

    How do gravitational waves in spacetime stretch and compress solid matter such as the LIGO experiment. I ask this because the expansion of spacetime of the Universe doesn't seem to have any effect on the small scale ie the solar system.
  22. B

    Understanding Taylor Expansion near a Point

    I'm just trying to understand how this works, because what I've been looking at online seems to indicate that I evaluate at ##\delta =0## for some reason, but that would make the given equation for the Taylor series wrong since every derivative term is multiplied by some power of ##\delta##...
  23. J

    I What is the acceleration of the expansion of the Universe?

    I can't find any values of acceleration or rate of change of acceleration of the expansion of the universe when I looked it up and I need these values for a theory I'm working on that could supersede dark energy and show the universe is closed even if everything accelorating away from us and...
  24. Anmoldeep

    Expanding explosion from an Asteroid

    An asteroid of mass M explodes into a spherical homogenous cloud in free space. Due to energy received by the explosion, the cloud expands and the expansion is spherically symmetric. At an instant, when the radius of the cloud is R, all of its particles on the surface are observed receding...
  25. M

    B Space-Time Expansion: Objects Accelerating Without Force?

    I am familiar with the concept of the curvature of space-time. I imagine that space-time can also expand. If this is possible then objects far from our view may appear to accelerate. No force required they are traveling through space that is changing in curvature or expanding. Is this a...
  26. L

    Finding the increase in entropy of the universe in gas expansion

    a) ##P_f=\frac{nRT_f}{V_f}=\frac{nR\frac{T_i}{2}}{2V_0}=\frac{1}{4}\frac{nRT_i}{V_0}=\frac{1}{4}P_i## b) ##Q=\Delta U=nC_V \Delta T=n\frac{5}{2}R(-\frac{T_i}{2})=-\frac{5}{4}nRT_i=-\frac{5}{4}P_i V_0## (##L=0## since the gas expands in a vacuum;Now, (a) and (b) are both correct but not (c), for...
  27. Chestermiller

    I Expansion or Compression Work by Gas ##=\int{P_{ext}dV}##

    In private discussions, another member @burian and I have been discussing why, in compression and expansion of a gas, the work can be calculated from ##W=\int{P_{ext}dV}##. We thought it would be of value to open the discussion to the full membership. Burian last asked about: When the...
  28. J O Linton

    B What is the distance at which gravity and the cosmological force are equal?

    In considering the excellent answers given to my previous query about a photon in a box, I was led to consider what force was needed to hold the walls of the box stationary (w.r.t. an inertial observer inside the box.). If you place a mass m on the end of a very long string of inextensible...
  29. T

    I How do we know that red-shift is caused by expansion?

    Hi, I am not a cosmologist, but this question has been bugging me for some time. I am an engineer, and I own an aquarium, at least I owned an aquarium with an awesome LED light. Under certain conditions, I found that when the blue night light was on, organics in the water would fluoresce, green...
  30. ergospherical

    A Geodesic Expansion: Finding the $\theta_{\pm}$ Factor

    \begin{align*} \mathrm{\mathbf{(a)}} \quad U_{\pm} \cdot U_{\pm} &= \dfrac{1}{2} (n_a n^a \pm 2 n_a m^a + m_a m^a) = \pm n_a m^a = 0 \\ U_+ \cdot U_- &= \dfrac{1}{2} (n_a n^a - m_a m^a) = \dfrac{1}{2} (-1-1) = -1 \\ \\ \mathrm{\mathbf{(b)}} \quad P^a_b &= \delta^a_b + U_{\mp}^a (U_{\pm})_b +...
  31. J

    B Hubble Expansion & GR Universe Size Predictions: Exploring Forces & Results

    Consider a celestial object distance d1 away from an observer, receding at v1=H0d1, Fig.a. And the same object at some time later, now at distance d2 and receding at higher speed v2=H0d2, Fig.b -- 1) where does the accelerating force come from? 2) the resulting universe-size vs time...
  32. Mike holden

    B Accelerating Universe Expansion: Age & Hubble Constant

    In my article - The accelerating expansion of the Universe at: [Unacceptable reference delted by the Mentors] I discuss how the age of the Universe depends on the rate of acceleration, the common factor being the value of the Hubble Constant at the present time. I go on to show how the expansion...
  33. Gannet

    I Acceleration of Universe Expansion: 1/r2

    It seems to me as the space between galaxies expands it reduces the gravitational attraction between them. Assuming that this is happening between the majority of the galaxies in our Universe it would cause the acceleration of expansion by a factor of 1/r2.
  34. SilverSoldier

    Thermal Expansion of a Triangular Frame

    Suppose each side has initial length ##l##. The solution taught to me is as follows. Considering the lengths of the rods after expansion, we write $$\dfrac{3l^2}{4}\left(1+\mu\theta\right)^2+\dfrac{l^2}{4}\left(1+\alpha\theta\right)^2=l^2\left(1+\lambda\theta\right)^2$$ according to the...
  35. J

    Relationship of Modulus to thermal expansion

    I'm trying to figure out how to relate expected thermal expansion of a uv cured polymer within a rigid cylinder to a modulus specification. The issue is the expected change in refractive index due to thermal expansion. The expansion coefficients are not available. Anybody have an idea. Do...
  36. C

    A Has anybody programmed the mcKL expansion?

    Hello everyone. I am trying to implement the mcKL expansion proposed in this article using Matlab and two vectors of correlated data of size 1000*50, meaning 50 realizations of two random processes measured 1000 times. As the article says, if two stochastic processes are correlated, one cannot...
  37. J

    B Cosmological constant for the Universe's expansion

    Astronomers1) tell us that a 'cosmological constant' can account for the universe's increasing expansion. Representing the universe by a symbolic expanding ring, Fig.a, at an instantaneous radius r the inward gravitational force varies as the inverse square of this radius, giving Fg ~ 1/r^2...
  38. C

    MATLAB Problem with Karhunen-Loève expansion in matlab

    I have copied the code of the accepted answer to this post in the official Matlab forums, since I am interested in performing the KL expansion myself. clc clear all y=[1,2,4;2,3,10]; y=y' %Reasons for transposing will become clear when you will read the second point given below...
  39. Amir Sedieqy

    Expansion Joint Connection to storage tank

    Hello, In a piping system connected to the outlet of an crude oil tank, process man has located the expansion joint after the valve which is connected to tank's nozzle. Since this expansion joint is located after the valve, it must be able to withstand the design pressure of the piping system...
  40. S

    B The Fate of the Universe -- Expansion or Collapse?

    If galaxies are now expanding away faster than light, then how would we know if this has now started to slow, stop and or reverse ? Is there a chance we may never know and the universe collapse won't be seen coming ?
  41. E

    A Operator Product Expansion as shown in Schwartz

    I have included here the screen shot of the page I am referring to.I am unsure of how this non-local Lagrangian of Eqtn(32.68) has been constructed. Have they just integrated the interaction Lagrangian densities over two different sets of points (x & y) ? If so, then why is there no P_L in...
  42. H

    B Term for an end state of expansion?

    Whereas a singularity is everything together, is there a name for a proposed end state after a Big Bang or something similar? Is there a name for that situation (hypothetical or not) where each elemental particle is so far from every other elemental particle that nothing affects anything...
  43. MathematicalPhysicist

    Mathematica Series expansion from the red book on special functions by Richard Ask

    I want to check my calculations via mathematica. In the book I am reading there's this expansion: $$\frac{(1+\frac{1}{j})^x}{1+x/j}=1+\frac{x(x-1)}{2j^2}+\mathcal{O}(1/j^3)$$ though I get instead of the term ##\frac{x(x-1)}{2j^2}## in the rhs the term: ##-\frac{x(x+1)}{2j^2}##. So I want to...
  44. D

    Tracking thermal expansion of an aluminium load cell

    Hi all, I am having trouble getting repeatable results from a linear regression formula that simply uses temperature vs load cell output especially with rapidly increasing/decreasing temperatures. This appears to be a result of the thermal co-efficient of our temperature sensor being almost...
  45. J

    Linear Expansion - Finding temperature

    So if I am understanding the question correctly, I need to find the change in temperature that causes one rights outer radii to be the same as another rings inner radii. Now what I tried is two equations change length_1= a_1*original length_inner * change in temp change length_2= a_2*original...
  46. AN630078

    Coefficients in the expansion of (1+x)n in A.P, find n

    https://www.toppr.com/ask/question/if-in-the-expansion-of-1-xn-the-coefficient-of-14th-15th-and-16th/ https://www.sarthaks.com/402983/if-in-the-expansion-of-1-x-n-the-coefficients-of-14-th-15-th-and-16-th-terms-are-in-a-p-find-n Specifically regarding my problem the coefficients of x^8, x^9 and...
  47. LCSphysicist

    I How to compute the expansion of this congruence?

    ##u^{a}\partial_{a} = (1-3M/r)^{-1/2}(\partial_{t} + (M/r^3)^{1/2} \partial_{\theta})## in Schwarzschild metric. I need to compute the expansion of this vector field, but i am not sure how. Adopting the fact that ##u_{a};_{b} = B_{ab} (1)##, i want at first to construct the B matrix, but i am...
  48. C

    I Expansion of a complex function around branch point

    I’m coming at this question with a physics application in mind so apologies if my language is a bit sloppy in places but I think the answer to my question is grounded in math so I’ll post it here. Say I have a function F(z) defined in the complex z plane which has branch points at z=0 and z =...
  49. Doshke

    Coefficient of volumetric expansion of gasoline at different temperatures

    I tried to solve the task in different ways, I had different ideas but none of them led me to the correct solution. I would be grateful if someone would explain at least the initial part of the task to me. True answer: 10-3K-1
  50. Z

    Entropy change for spontaneous/ irreversible gas expansion

    When trying to describe why the entropy goes up for a irreversible process, such as gas expanding into a vacuum, it seems fairly easy at a high level. the valve between the two chambers opens, the free expansion occurs, the pressure drops proportional to the volume change and the temp remains...
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