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

    Problem with series convergence — Taylor expansion of exponential

    Good day and here is the solution, I have questions about I don't understand why when in the taylor expansion of exponential when x goes to infinity x^7 is little o of x ? I could undesrtand if -1<x<1 but not if x tends to infinity? many thanks in advance!
  2. R

    Engineering Thermal expansion coefficient calculation — where is my mistake?

    Hello everyone, Once I got through the VDW state equation I came to the expression of the thermal expansion coefficient. When I place the values I get an illogical answer. Is there a problem with the units? (Please ignore the values) Thanks. This is the unit equation I get to and get stuck:
  3. A

    I Taylor expansion of an unknown function

    Hello, I have a question regarding the Taylor expansion of an unknown function and I would be tanksful to have your comments on that. Suppose we want to find an analytical estimate for an unknown function. The available information for this function is; its exact value at x0 (f0) and first...
  4. L

    Thermodynamics: gas expansion formula or approximation error?

    FIRST TYPE: REVERSIBLE PROCESS At the temperature of 127 ° C, 1 L of CO2 is reversibly compressed from the pressure of 380 mmHg to that of 1 atm. Calculate the heat and labor exchanged assuming the gas is ideal. Q = L = - 34.95 J CONDUCT 380 mmHg = 0.5 atm L = P1 * V1 * ln (P1 / P2) = 0.5 * 1...
  5. jjson775

    Expansion of the Universe -- By what factor will the distance between remote galaxies increase in the future?

  6. E

    Linear expansion of steel versus copper with increasing temperature

    Here I'm going to show all that I've understood - 1. 2. 3. What I've attempted - L = Lo (1+ α * ẟT) ẟT = 150°C - 15°C = 135°C (Steel) L = ẟL (1 + 11 * 10^-6 * 135) (Copper) L = ẟL (1 + 17 * 10^-6 * 135) This doesn't get me anywhere, obviously. Am I supposed to understand from the...
  7. R

    Engineering Heat Capacity and the Coefficient of thermal expansion

    thanks!
  8. S

    Find the middle terms of this binomial expansion

    I know how to expand it. My question is: the expansion has 8 terms so what would be the middle term? Will the answer be "the expansion has no middle term"? Or maybe seeing the phrase of the question (middle terms), there will be two answers (the 4th and 5th term)? Thanks
  9. JD_PM

    I Solution Expansion of ##A^{\mu}## when ##L \rightarrow \infty##

    Please note that I'll write ##A^{\mu} := A^{\mu}(x)## for simplicity. I'll work in natural units. The Lagrangian density ##\mathscr{L} = -\frac 1 2 (\partial_{\mu} A_{\nu})(\partial^{\mu} A^{\nu})## has equations of motion $$\Box A^{\mu}=0 \tag{1}$$ We expand ##A^{\mu}## in a complete set...
  10. J

    Help with 2nd order Runge Kutta and series expansion

    So here's my homework question: This is the reference formula along with the Rung-Kutta form with the variables mentioned in the question Here is my attempt so far: Problem is that i am unsure how to expand this to even get going. I tried referencing my text Math Methods by Boas which has...
  11. qnach

    Jackson Classical Electrodynamics: page 35 expansion of charge

    Could anyone explain how did Jackson obtain the Taylor distribution of charge distribution at the end of section 1.7 (version 3)?
  12. Jehannum

    Best way to measure non-thermal expansion of a pipe

    Ideally, the method should be accurate down to 0.01 millimetres or better. We're probably talking pipes of up to 150 mm (6") diameter. Accurately measuring the actual diameter of the pipe is of less importance - it's how much it expands that matters. My idea is wrapping something around the...
  13. ShayanJ

    A Developing the Feynman diagram expansion

    I'm reading "introduction to many body physics" by Piers Coleman. In section 7.2 he's trying to introduce Feynman diagrams by expanding the generating functional. But first he transforms it into this pictorial form: Then he calculates the n=1, m=1 term like below: Which I understand. But I...
  14. jk22

    B Why expansion of a gas implies cooling?

    Normally expansion implies colding, but I don't know how to explain this with the equation of perfect gazes : ##PV=nRT## If V increase then the pressure diminishes. Admitting a constant number of molecules, is the number of shocks is inversely proportional to the volume ? But this only implies...
  15. rannasquaer

    MHB Thermal Diffraction and Expansion

    Does anyone know how I can relate the diffraction in a circular crack to the thermal expansion of that crack? Something that I relate the gap radius with the distances between the light and dark fractions of the diffraction figure.
  16. AN630078

    Binomial Expansion: Evaluating Coefficient from two binomials

    So I think I may be overcomplicating this problem but I realize that in order to find the x^3 term it will be the product of the two binomials, ie. x^1*x^2=x^3. The coefficient of x^3 will be the coefficient of x^1 in the first bracket multiplied by the coefficient of x^2 in the second bracket...
  17. C

    A How are the thermal expansion of a solid and the stress tensor related?

    My idea is this: tensor stress is directly related to the internal pressure of a solid. That is to the force that the neighboring atoms exert each other in relation to a unit of surface. When I heat a solid we can have the phenomenon of thermal expansion: this is connected to the fact that a...
  18. T

    A Accelerated Hubble expansion -- Is the second derivative positive?

    Since distances increase, their first derivative which is velocity (Hubble constant) should be positive if not increasing too. Accelerated expansion needs the velocity to increase. What about the third derivative which is acceleration? An accelerated universe could have third derivative (called...
  19. E

    B The accelerated expansion of the universe; redshift and time/distance

    I am certain that my confusion here rests in a misunderstanding on my part and not in a mistake having been made by countless physical theorists. Nevertheless, I have had a hard time wrapping my head around it. Here is the crux: We observe that light from distant objects is more redshifted...
  20. Tony Hau

    What is the meaning of r' in the Multipole Expansion?

    The diagram of the problem should look something like this: ,which is just the normal spherical coordinate.To calculate the potential far away, we use the multipole expansion. ##I_o## in the expansion is ok, because ##(r^{'})^{0} = 1##. However, I am wondering how I should calculate ##I_1##...
  21. Hiero

    Adiabatic expansion of a piston in a cylinder filled with ideal gas

    I was puzzling over how to solve this and finally peeked at the solution. They used the relevant equation above. I disagree with this though. The problem specifically says “the piston is allowed to slide freely!” This means that we don’t let it happen slowly. So then we are not in...
  22. Rahulx084

    How Does Joule Thomson Expansion Affect Gas Temperature?

    Wikipedia says, Unlike a free expansion , in Joule Thomson expansion work is done causing the change in internal energy. Whether the internal energy increases or decreases is determined by whether work is done on or by the fluid; that is determined by the initial and final states of the...
  23. Ron19932017

    Euler's equation of thermodynamics in free expansion (Joule expansion)

    Hi everyone, I am confused when I apply Euler's equation on the free expansion of an ideal gas. Consider a free expansion (expansion of gas in vaccum) where the volume is doubled (V->2V) The classical free expansion of an ideal gas results in increase in entropy by an amount of nR ln(2), a...
  24. Adesh

    Analysis Books for learning Fourier series expansion

    Hello Everyone! I want to learn about Fourier series (not Fourier transform), that is approximating a continuous periodic function with something like this ##a_0 \sum_{n=1}^{\infty} (a_n \cos nt + b_n \sin nt)##. I tried some videos and lecture notes that I could find with a google search but...
  25. Chestermiller

    Going from 1st state to 2nd through irreversible isothermal expansion

    My teacher was teaching me that how work done in isothermal reversible expansion is greater than irreversible expansion and also work done in isothermal irreversible compression is greater than that for reversible compression. He then said if someone tries to go from 1st state to the 2nd step (...
  26. M

    B Expansion of the Universe and the fourth dimension

    The perimeter of a circle increases by radius, the surface area of a ball increase by radius(which is height which is the third dimension if the ball is a planet like the Earth), and the universe is expanding by time, can we say that the fourth dimension is time by this ?
  27. JD_PM

    Series expansion of the Lorentz Transformation

    a) I think I got this one (I have to thank samalkhaiat and PeroK for helping me with the training in LTs :) ) $$\eta_{\mu\nu}\Big(\delta^{\mu}_{\rho} + \epsilon^{\mu}_{ \ \ \rho} +\frac{1}{2!} \epsilon^{\mu}_{ \ \ \lambda}\epsilon^{\lambda}_{ \ \ \rho}+ \ ...\Big)\Big(\delta^{\nu}_{\sigma} +...
  28. R

    Expansion in non-adiabatic Otto / Diesel cycles

    Hello! I have a question that has been bothering me for a while now. If we look at the expansion step of a real otto or diesel cycle we see that while the pressure drops to near surrounding levels the temperature remains relatively high ( high T of the exhaust gas). How is that possible? How...
  29. R

    I Non-adiabatic expansion in Diesel and Otto cycles

    Hello! I have a question that has been bothering me for a while now. If we look at the expansion step of a real otto or diesel cycle, we see that while the pressure drops to near surrounding levels, the temperature remains relatively high ( high T of the exhaust gas). How is that possible? How...
  30. Matilda111

    B Research Paper: Exploring Decay in c Due to Universe Expansion

    I'm currently writing a research paper about the speed of light. I have researched universe expansion, specifically, the quantised redshift spectral index fluctuations of distant galaxies and other structures over time, however, I need to suggest why universe expansion possibly causes a recorded...
  31. G

    How to expand this ratio of polynomials?

    I could simplify the expressions in the numerator and denominator to (1+x^n)/(1+x) as they are in geometric series and I used the geometric sum formula to reduce it. Now for what value of n will it be a polynomial? I do get the idea for some value of n the simplified numerator will contain the...
  32. Coltrane8

    I Spherical Harmonics Expansion convergence

    In the contex of ##L^2## space, it is usually stated that any square-integrable function can be expanded as a linear combination of Spherical Harmonics: $$ f(\theta,\varphi)=\sum_{\ell=0}^\infty \sum_{m=-\ell}^\ell f_\ell^m \, Y_\ell^m(\theta,\varphi)\tag 2 $$ where ##Y_\ell^m( \theta , \varphi...
  33. C

    I Does the expansion of the Universe affect orbiting bodies?

    Does the expansion of the universe affect orbits? Would the orbits of the Magellanic Clouds, for example, be different if the universe were not expanding? If orbits are affected, at what scale do we first detect the effects?
  34. T

    What does the thermal expansion lab data reveal?

    So guys I had physics lab where we used Steam Generator, Pasco interface and Capstone. In a nutshell there is graph attached below and formula, please write the solution with this formula.
  35. A

    Is Entropy decreased for Free expansion of a Waals gas?

    Previous of this problem, there was another problem. that is "What is the change in Temperature of van der Waals gas in free expansion?". I got them. It was C_V dT= -aN^2/V^2 dV Then, I got T=T0-aN^2/2VC_V So i knew that the Temperature is decreased by free expansion in adiabatic process. Then I...
  36. N

    Shrinkage & Expansion of plastic parts

    Hi, I'm currently doing a shrinkage study upon this plastic part. I hv been observing how much can the part able to shrink over the time after molding, and now hv been on the 5th month observation. However, on the 5th month, the part starting to expand, compared with the data from the 4th...
  37. A

    How to caluculate the pressure immediately downstream of a sudden expansion

    Good day All Here is the first ligne of the exercice that might not be visible As shown in figure , water (kinematic viscosity of water v=1E-6 m2s-1)flows out of a reservoir with a sharp entrance at A. My questions is how to compute the pressure pn right down stream the sudden expansion My...
  38. M

    I How Is Entropy Calculated in an Irreversible Gas Expansion?

    Hi, An irreversible gas expansion is often described in textbooks with a compressed gas in a cylinder pushing up a weight (with mass m) via a hypothetical friction-less and weightless piston. It is said the work done by the gas is equal to -mg × h and from this you can derive the work for a...
  39. O

    I Is My Basic Understanding of Universe Expansion Correct?

    Summary:: I would like clarification about universe expansion. Hello I would first like to see if my entry level understanding of how the expansion of the universe is obtained or measured. (In a very basic model or example) First: My current understanding is that one way the distance to...
  40. I

    Infinite Square Well Expansion: Mass m in Ground State

    A particle of mass m is in the ground state on the infinite square well. Suddenly the well expends to twice it's original size (x going from 0 to a, to 0 to 2a) leaving the wave function monetarily undisturbed. On answering, for ##\Psi_{n}## I got ##\Psi_{n}## = ##\sqrt{\frac{1}{a}}...
  41. Avaro667

    A Elliptic trigonometric functions as basis for function expansion ?

    Hey everyone . So I've started reading in depth Fourier transforms , trying to understand what they really are(i was familiar with them,but as a tool mostly) . The connection of FT and linear algebra is the least mind blowing for me 🤯! It really changed the way I'm thinking ! So i was...
  42. H

    I Does the expansion of the Universe heat stars and bodies?

    The expansion of space is about 68 km/s/Mpc, or 0.00002 km/s/light year. The radius of the sun is about 700000 km. Thus, initially ignoring additional forces, the change in radius of the sun due to the expansion of space is about 1.5*10^-9 m/sec, or 5 cm/year. I assume that this expansion is...
  43. Killtech

    I Probability density expansion

    This is probably a stupid question but i don't want to make a stupid mistake here, so i thought better ask: I'm starting with the simple free Schrödinger Equation ##V(x)=0## (can be 1 dim) and an initial condition where the wave function is somehow constrained to be entirely localized around a...
  44. S

    Taylor expansion of an Ising-like Hamiltonian

    For the case when ##B=0## I get: $$Z = \sum_{n_i = 0,1} e^{-\beta H(\{n_i\})} = \sum_{n_i = 0,1} e^{-\beta A \sum_i^N n_i} =\prod_i^N \sum_{n_i = 0,1} e^{-\beta A n_i} = [1+e^{-\beta A}]^N$$ For non-zero ##B## to first order the best I can get is: $$Z = \sum_{n_i = 0,1}...
  45. C

    I Finite expansion of a fraction of functions

    I am having a problem finding the right order above and below to find the finite expansion of a fraction of usual functions assembled in complicated ways. For instance, a question asked to find the limit as x approaches 0 for the following function I know that to solve it we must first find...
  46. jisbon

    Thermal expansion (surface area)

    Hi all, For area expansion, I know the equation goes like: Hence, my answer to part i is ##\begin{aligned}A=A_{0}\left( 1+2\alpha \Delta T\right) \\ = 52\left( 1+2*24\times 10^{-6}\right) \left( 100\right) \\ =52.2496cm^{2}\end{aligned} ## Now I am unsure how to proceed with part 2 in this...
  47. K

    I Questions about the expansion of space on galactic scales

    How would the expansion on a scale of 10 kpc be measured, by a red or blue shift? How can expansion of space be differentiated from the velocity of stars? It seems that the expansion of space weakens the effects of gravity?
  48. Robin04

    I Matter movement versus spacetime expansion

    If I understood well, cosmology makes a difference between matter moving in spacetime and the expansion of spacetime itself. Are these concepts experimentally distinguishable, or this distinction is only in our theories?
  49. Y

    Temperature change in a gas expansion

    1- ##\delta P_V =(\frac{\partial P}{\partial T} )_V \delta T_V## 2-##\delta V =(\frac{\partial V}{\partial T})_P \delta T+(\frac{\partial V}{\partial P})_T \delta P## so ##C_v \delta T=-P\delta V=-P((\frac{\partial V}{\partial T})_P \delta T+(\frac{\partial V}{\partial P})_T \delta P)## I can...
  50. NP04

    Linear Thermal Expansion with respect to time

    ΔL= αLoΔT ΔL = (23*10^-6)(0.2480 m)(28.30°C) ΔL = 1.61 * 10^-4 Period is 1s, so each second the pendulum moves 1.61 * 10^-4 m 1.61 * 10^-4 m/s *(60s/1min)*(60min/1hr)*(24hr/1day) = 13.95 m/day T = s (1:1 ratio) 13.95 seconds. But the answer is actually 69.3 s. Is the equation T = 2π√L/g...
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