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. Philip Koeck

    The exact formula for PV-work in an irreversible process

    I've written a short text adapted from a previous post by Count Iblis. I'll append it below. It shows that irreversible PV-work is always smaller than reversible, which fits very nicely with W = Pext ΔV. I'd be interested if there's a way to show that W is exactly equal to Pext ΔV for all...
  2. Ben Geoffrey

    I Taylor Series Expansion of Quadratic Derivatives: Goldstein Ch. 6, Pg. 240

    Can anyone tell me how if the derivative of n(n') is quadratic the second term in the taylor series expansion given below vanishes. This doubt is from the book Classical Mechanics by Goldstein Chapter 6 page 240 3rd edition. I have attached a screenshot below
  3. J

    What happens to the angle of a circular ring as temperature increases?

    Homework Statement A part of a circular ring is missing .What happens to the angle when temperature is increased ? 1) θ increases 2) θ decreases 3) θ remains same 4) θ increases initially but becomes constant after a particular temperature . Homework EquationsThe Attempt at a Solution As...
  4. J

    Thermal expansion of air inside a bottle -- some questions....

    For thermal expansion in a bottle - is there a theoretical model on the pressure exerted on the inside of the bottle due to the air inside expanding when the bottle heats up. The air will be expanding randomly in all directions so the pressure exerted at any point on the inside of the bottle...
  5. T

    Is this Gas Expansion Problem a Quasi-Static Adiabatic Process?

    MODERATOR'S NOTE: Moved from other forum, so no template @Chestermiller I am still having trouble figuring out if a given process is Quasi-static or not. Consider the following case. The cylinder consists of an ideal gas at the bottom and a liquid of density ρ at the top separated by a piston...
  6. C

    B Measuring the Universe's expansion rate

    From our perspective the Universe is expanding faster the further away things get, correct? Given that we are measuring further and further back in time my question is this. If you were at the furthest known point in the Universe looking back at our galaxy and attempting to measure the expansion...
  7. C

    Polynomial expansion from Python to Mathematica

    Hi everybody. In Python there is a library called chaospy. One useful command is cp.orth_ttr which generates a polynomial expansion, e. g. a series of orthogonal polynomials or orders zero, one, two... for a random variable e.g normal, uniform... For more information see...
  8. M

    I Which x_0 to use in a Taylor series expansion?

    I already learn to use Taylor series as: f(x) = ∑ fn(x0) / n! (x-x0)n But i don´t see why the serie change when we use differents x0 points. Por example: f(x) = x2 to express Taylor series in x0 = 0 f(x) = f(0) + f(0) (x-0) + ... = 0 due to f(0) = (0)2 to x0=1 the series are...
  9. ertagon2

    MHB Integration by parts, Partial fraction expansion, Improper Integrals

    - check if right check if right Now, 2 seems to be the right answer for A yet when i made x=5 and subtracted new form form the old one I got a difference of ~$\frac{4}{9}$ (should be 0 obviously) I got A=2 B=$\frac{45}{21}$ C=2 How to calculate $\lim_{{x}\to{\infty}}(- e^{-x})$
  10. B

    Compression and Expansion of a Volume of Air

    Homework Statement Air with an initial volume of 0.12m³, pressure 1 bar and temperature 18°C is compressed according to the law pV1.3 = c through an 8:1 compression ratio. It is then allowed to expand isothermally back to its initial volume. Determine: i) the pressure and temperature after...
  11. D

    B Accelerated expansion of the universe

    If a big bang could occur at a point in space-time, couldn't we at least speculate that many big bangs could have occurred at many other points in space time, and could have resulted in many parrelel universes evolving far away or in close neighborhood of our own one? And then, could it not be...
  12. K

    B Dark energy causing universe expansion?

    What is the dark energy which apparently is causing the expansion of the universe to accelerate?
  13. G

    B Black holes and universe expansion

    As we know the universe is expanding. Could this accelerating expansion contribute or cause black hole evaporation given that the strength of the gravitational force does not depend directly on time, while the distance of two given points in space increases with time? Sorry if my approach is...
  14. N

    Laplace expansion of the inner product (Geometric Algebra)

    Homework Statement Prove that ##\vec {a} \cdot (\vec {b} \wedge \vec {C_r}) = \vec {a} \cdot \vec {b} \vec {C_r} - \vec {b} \wedge (\vec {a} \cdot \vec {C_r})##. Note that ##\vec {a}## is a vector, ##\vec {b}## is a vector, and ##\vec {C_r}## is an r-blade with ##r > 0##. Also, the dot...
  15. J

    I Normalisation constant expansion of spinor field

    Hi, I'm reading about the wave packet solution to the dirac equation but in the book I'm reading it states that \int \frac {d^3p} {(2\pi)^3 2E} [a u e^{-ipx} + b^\dagger \bar{v} e^{ipx} The normalisation constant confuses me. I guess the 2pi^3 is reasonalbe. However, the 1/2E seems a bit...
  16. binbagsss

    Order of zero of modular form from its expansion at infinity

    1. Homework Statement order of zero of a modular form ? 2. Homework Equations 3. The Attempt at a Solution Apologies if this is a stupid question but I'm pretty confused. So, a modular form ##f(t) \in M_k ## is usually given by it's expansion about ##\infty## expressed in the variable...
  17. J

    A QFT Field Expansion: Explaining (2.72) - Schwartz

    The attached pic is from Schwartz. Can someone explain the second equality sign in (2.72)?
  18. Jo MacDonald

    Does the Coefficient of Thermal Expansion Apply to Both Expansion and Contraction?

    We did an activity today in class where we placed an empty 2L bottle in the Freezer, let it contract, then calculated the coeffcient of volumetric expansion using ΔV = VoβΔT. We got pretty close to the accepted value. The question is... Does the coefficient of thermal expansion only work for...
  19. C

    Thermal Expansion to Retain a Bolt

    I have 1" aluminum rod and I want to dril a hole in a steel structure for the bolt. If I have a 1" drill and take .001" inches off of it at the machine shop, so that it is now 0.998 inches, there will have to be about a 200°C difference in temperature between the two articles (aluminum...
  20. binbagsss

    Product of modular forms: poles, zeros expansion

    Homework Statement question concerning part c. Homework Equations The question is pretty simple if there is no zero of order ##N## at infinity, such that it does not cancel the pole of ##f(t)## at infinity of order ##N##. In this case it follows that ## f(t) g(t) \in M^{!}_2 ## and so we...
  21. CJ2116

    Binomial Expansion (Arfken/Weber/Harris 1.3.9)

    Hi everyone, I'm currently working through Mathematical Methods for Physicists 7th ed. by Arfken/Weber/Harris and there's one question that's been giving me some difficulty. I would appreciate any feedback if possible. Thanks! Chris Homework Statement The relativistic sum w of two...
  22. S

    I Gravitational Waves vs Universe Expansion Rate

    Is there any relationship between the Speed of gravitational waves and the Universe's "local" expansion rate? Speed of gravitational waves is supposed to be equal to the speed of light. Gravitational waves don't travel faster than light. But we can observe far galaxies moving away from us with...
  23. M

    Enthelpy in Throttle Process (Joule–Thomson expansion)

    Why is it written that enthalpy (##H##) is constant for Joule-Thompson expansion? It seems the essence of this process is to convert from one pressure to another with no heat loss. How does that connect with enthalpy being constant? When I learned about enthalpy it seemed to be most relevant to...
  24. Souhardya Nandi

    I Is Gravitation Responsible for the Stability of the Universe?

    In the universe, there are several celestial bodies, all of which attract each other. Then why is it so that they do not collapse towards each other. Is it a consequence of expansion. If so, will a change in acceleration of expansion have any effect on it.And can then this be considered a...
  25. PeppaPig

    Thermal expansion of bimetallic strip

    Homework Statement [/B] A bimetallic strip is made of metal which has coefficient of thermal expansion is equal to α1 and the other's is equal to α2 at the temperature of T0. The temperature is increased to T0 + ΔT (ΔT > 0). The strip curves as shown in the figure. If both strip have the same...
  26. F

    Isothermal Expansion: Explained

    I am a little confused by the following; When an isothermal expansion takes place there is negative work done on the gas by the pressure, this I understand. Now by the first law the change in internal energy is equal to the heat transferred to the gas plus the work done it. So now in my script...
  27. Paul Howard A

    I Is Expansion of Space Affecting Gravitational and Nuclear Forces?

    I was thinking about the expansion of space. It seems clear that objects that are bound by gravitation or the strong nuclear force do not experience an increase in size as the universe continues it's expansion. However, such systems do contain abundant space. It is argued that gravitation and...
  28. fresh_42

    I Is the Friedmann Space-Time Observable Without Dark Energy?

    I'm not quit sure whether we had this paper here already, since it is a couple of weeks old. I've seen it here https://phys.org/news/2017-12-dark-energy-mathematicians-alternative-explanation.html and I'm somehow fascinated by the idea to get rid of dark energy as only explanation of current...
  29. M

    A Matched Asymptotic Expansion and stretching variables

    Hi PF! Regarding matched asymptotic expansions, given an ODE BVP, I have learned a boundary layer can arise, where we need to stretch the independent variable through carefully selection i.e. if ##x## is the independent variable, perhaps ##\phi = (1-x)/\epsilon : \epsilon \ll 1##. Would we...
  30. T

    I Expansion Rate of Cosmic Bubbles

    I’ve understood that within the theory of Eternal Inflation the Bubble Universes that form from a drop of “vacuum” energy expand at the Speed of Light. My question is: Why would expansion be at the speed of light and not at a speed proportional to the level of vacuum energy still present in...
  31. S

    Fourier Series Expansion

    Homework Statement There is a sawtooth function with u(t)=t-π. Find the Fourier Series expansion in the form of a0 + ∑αkcos(kt) + βksin(kt) Homework Equations a0 = ... αk = ... βk = ... The Attempt at a Solution After solving for a0, ak, and bk, I found that a0=0, ak=0, and bk=-2/k...
  32. T

    Understanding Expansion Fans and Reflected Waves in Propulsion Systems

    "For simplicity, let us assume the flow turns around a corner downstream of the throat, where the Mach number is M0 > 1, to an angle θ1, and let us indicate just three of an infinite number of waves making up the "expansion fan". Since the centerline is an axis of symmetry, the waves must...
  33. M

    Adiabatic expansion problems

    Homework Statement I do not know if I am allowed to have two question in one post, so forgive me if I am breaking a rule. These two are frustrating me as I cannot see where the error in my process is. 1) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 10 ∘C, expands...
  34. Souhardya Nandi

    I Will the acceleration of the expansion of universe ever decrease?

    This may sound like a noob question but please help me out guys.Will universal acceleration ever retard ? And if it continues to accelerate for all eternity, where is it getting this never ending energy from ?
  35. Mayed Al-Tunaiji

    I Time & Space Expansion: High Schooler Qs

    Before I get to a question that's been on my mind for a while, I would like to make it clear that I am a high school student with no understanding of physics beyond my school's curriculum and some books that I've read, so excuse me if this sounds rather absurd. I know that the expansion of...
  36. R

    B What if the universe's expansion is actually slowing down?

    Hello guys, every "scientist" I have talked to say the universe is "expanding" at an ever increasing rate. then I tell them the following: "hey man, you say the farther away the galaxies you see, the quicker away from us they are moving, right ? (redshift, etc)" they say: "yeah" then I say...
  37. M

    Isentropic Expansion Within a Steam Turbine System

    Homework Statement Steam is expanded from 90 bar, 412°C to 4.0 bar saturation in a high pressure turbine, after-which a certain percentage of the steam is bled off to a feed heater. The remaining steam is then expanded through a low pressure turbine to 1.0 bar and dryness fraction of 0.93. All...
  38. Ranku

    I Cosmological constant and rate of expansion of the universe

    Does the presence of the cosmological constant modify the rate of expansion of the universe even during the earlier deceleratingly expanding phase of the universe?
  39. Pericles98

    Internal energy during the expansion of a gas?

    I have question regarding the (W = ∫Pdv) formula for the work done during the expansion of an ideal gas and the change in internal energy during the process. If we were to have a gas enclosed inside an insulated cylinder with a movable piston at one end with cross sectional area "a", I...
  40. V

    Work done in expansion of a bubble

    Homework Statement as title Homework Equations force exerted by atmosphere on bubble = 2(on account of dual layer) * 2pi*r*L(surface tension) work is the integral of force *dx The Attempt at a Solution so we're looking at int ( 4pi*r*L *dr) but since not it 1 particle is traveling against...
  41. S

    Work and Volume in Adiabatic Expansion

    Homework Statement A sample of 1.60 mol H2 (Cv = 20.5 J K-1 mol-1) at 21°C and 1.50 atm undergoes a reversible adiabatic compression until the final pressure is 4.50 atm. Calculate the final volume of the gas sample and the work associated with this process. Assume that the gas behaves ideally...
  42. Joe Fatuch

    I How does the speed of light affect expansion acceleration?

    I may have a fundamental misunderstanding of the concept, but I was wondering, how does the accelerating expansion of the universe calculate for the time dilation in light travel? From my understanding, we know that the universe expansion is accelerating because the farthest galaxies that we...
  43. shihab-kol

    B Sun's Expansion: Why Inner Planets Will Be Affected

    I read in some books that as the sun approaches the end of the fusion process(the complete one) , it will expand and engulf some of the inner planets. But why will it expand?
  44. Adgorn

    I Understanding the Taylor Expansion of a Translated Function

    I recently found out the rule regarding the Taylor expansion of a translated function: ##f(x+h)=f(x)+f′(x)⋅h+\frac 1 2 h^ 2 \cdot f′′(x)+⋯+\frac 1 {n!}h^n \cdot f^n(x)+...## But why exactly is this the case? The normal Taylor expansion tells us that ##f(x)=f(a)+f'(a)(x-a)+\frac 1...
  45. M

    Asymptotic Expansion Exercise: Finding a Gaussian Point Solution

    Homework Statement Hi, i have this exercise and i have to find the asymptotic expansion on a gaussian point . Homework EquationsThe Attempt at a Solution [/B] I have transformed xt in et ln x in order to have the form used in the formula but ln x is not regular in 0 and it give some...
  46. T

    Maxwell Relation, Gibbs Free Energy, Thermal Expansion Coefficient

    Homework Statement By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. Homework Equations $$G=U-TS+PV$$ $$dG=\mu...
  47. T

    Maxwell Relation, Gibbs Free Energy, Thermal expansion

    By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny. My working:
  48. Xilus

    Exploring the Pressure of Heated Air and Water: Which Exerts More Force?

    Lets say you have a jar of water, and a jar of air. You heat both of them 100C will either of them explode? ok just kidding. which one exerts more pressure, and is hence more likely to explode? did heating the substance turn heat into force? (force per unit area)
  49. R

    B Understanding the Expansion of Space: Galaxies Moving Away and Proving Expansion

    How does knowing that galaxies are all moving away from each other and the farthest ones are moving more quickly prove that space is itself expanding and not just that the galaxies are moving through it?
  50. Ahmed Abdalla

    Why do we use Taylor expansion expressing potential energy

    My textbook doesn’t go into it, can someone tell me why Taylor expansion is used to express spring potential energy? A lot of the questions I do I think I can just use F=-Kx and relate it to U(x) being F=-Gradiant U(x) but I see most answers using the Taylor expansion instead to get 1/2 kx^2...
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