Expansion Definition and 1000 Threads

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. K

    Introduction to O(N) Model & Large N Expansion

    can anyone refer me to some good introduction to this O(N) model and also large N expansion. Thanks.
  2. S

    Discover the First Non-Zero Coefficient of e^-x Series Expansion | Homework Help

    Homework Statement Show that the first non-zero coefficient in the expansion of ##e^{-x}-\frac{1-x}{{\left(1-x^2\right)}^{\frac{1}{2}}{\left(1-x^3\right)}^{\frac{1}{3}}}## in ascending powers of x is that of x^5 Homework Equations Series expansion, logarithmic series The Attempt at a Solution...
  3. adoion

    Question about fluid expansion

    Hi, When a hot and dense fluid suddenly expands, how much can it cool down. Lets take for example an expansion valve from an AC, does the fluid do work when passing through the valve or does it not even need to do work in order to cool down. What is the lowest temperature that the fluid can...
  4. O

    Expansion of the Universe Question

    1: does the universe expand uniformly? 2: does galaxies closer to the calculated center expand faster or slower then galaxies further away? im asking because I am wondering on what drives the accelleration of the universe. there are many factors involved like dark matter, dark energy, photons...
  5. A

    Find the residue of g(z) at z=-2 using Laurent Expansion

    Homework Statement Find the residue at z=-2 for $$g(z) = \frac{\psi(-z)}{(z+1)(z+2)^3}$$ Homework Equations $$\psi(-z)$$ represents the digamma function, $$\zeta(z)$$ represents the Riemann-Zeta-Function. The Attempt at a Solution I know that: $$\psi(z+1) = -\gamma - \sum_{k=1}^{\infty}...
  6. T

    Exploring the Expanding Universe: Understanding the Stretching of Space-Time

    [Mentor's note: This thread was split off from https://www.physicsforums.com/threads/observable-universe-question.79096] The expansion of space can be likened to the stretching of the fabric of space time. At early epochs, that stretch was FASTER than the speed of light ... So the expansion...
  7. A

    Will a Rocket Reach a Distant Galaxy Moving Away Due to Space Expansion?

    First question. Suppose you send a rocket with initial speed of c/10 and no further propulsion or gravity to a distant galaxy moving away due to space expansion at a speed of c/3. Will the rocket reach the galaxy? Temptative answer. If we call f(t) the fraction of the distance covered at time...
  8. N

    Thermal Expansion of aluminium

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  9. K

    Potential from a simple Quadrupole expansion

    Hi everyone! I'm currently working on this problem for which I am getting inconsistencies depending on how I do it. I'm trying to find the potential due to the quadrupole moment of the following distribution: +q at (0,0,d), -2q at (0,0,0), and +q at (0,0,-2d) I am doing this using two...
  10. AdityaDev

    Why is P_ext different for reversible and irreversible isothermal expansion?

    I was able to derive the work done in a reversible isothermal expansion. There as the P changes to P-dP, the volume increases by dV and hence the internal pressure also decreases by dP and equilibrium is maintained. (Thanks to @Nugatory and @Chestermiller fo r explaining it). Now when we take an...
  11. binbagsss

    Limits FRW universe , rate of expansion, k=-1,0.

    Hi, I'm looking at deriving the limits of ##\dot{a}## as ## a-> \infty ## , using the Friedmann equation and conservtion of the ##_{00}## component of the energy momentum tensor for a perfect fluid. Both of these equations respectively are: ## \dot{a^{2}}=\frac{8\pi G}{3} \rho a^{2} + | k |##...
  12. G

    Counterterms in saddle point expansion

    In the saddle point evaluation of the path integral, at tree level, you plug in the classical solution of the field into the integrand. However, when determining the classical solution, we ignore counterterms. The counterterms only show up to renormalize divergences after a saddle point...
  13. nuclearhead

    Explaining Universe Expansion with Gravitons in String Theory/Supergravity

    In a theory like string theory or supergravity, gravity is described by gravitons on (usually) Minkowski background. But I don't see how this works in terms of the expansion of the Universe. For example, two galaxies far apart can be moving away from each other at more than the speed of light...
  14. M

    Series expansion for (e^x-1)/x

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  15. K

    Is the Maclaurin Expansion Valid for Infinite Points?

    my professor told me any n times differentiable function can be approximated by macularine/taylor expansion.is that true? As far as I know, if the function is approximated at point a, the approximation is valid if we pick a point near a. however, if we assume that we picked a point of...
  16. Nathanael

    Linear coefficient of thermal expansion

    The "coefficient of linear expansion" (≡k) was defined in my book by the following relationship: ##\Delta L=Lk\Delta T## Where L is length and T is temperature I'm wondering, is this just an approximation? Because, if you were to increase the temperature by \Delta T and then calculate the new...
  17. S

    MHB Series Expansion & l'Hopital's rule

    I'm preparing for my exam and have stumbled across this question. I understand how to execute the l'hopital's rule part of this but I just can't get there. I have no idea how to approach this in order to get a suitable series expansion to the 4th degree of x. Thank you
  18. R

    Expansion coefficients of a wave packet

    Homework Statement What are the expansion coefficients of a wavepacket \Psi (x) = \sqrt{\frac{2}{L}}sin \frac{\pi x}{L} in the basis Ψn(x) of a particle in a periodic box of size L? Homework Equations \Psi (r,t) = {\sum_{n}^{}} a_{n}(t) \Psi _{n}(r) The Attempt at a Solution \left \langle...
  19. C

    Work Done by Isothermal Expansion

    Homework Statement A quantity of ideal gas (0.800mole) at a pressure of 10.0atm and 200K is allowed to expand isothermally until it reaches a pressure of 1.00atm. Calculate the work done if this expansion is carried out a) against a vacuum, b) against a constant external pressure of 1.0atm and...
  20. B

    Facing problem in analysing Taylor series expansion

    This is a very basic question . Actually in Taylor series expansion of say "sin x" we write the expansion ... (as it is,I am not writing it) But when we are asked to write the expansion of sin(x^2) we just replace 'x' by "x^2" in the expansion of sin x. Or if asked some other function such as...
  21. AdityaDev

    How does heating a gas in a vessel with a piston affect the pressure inside?

    If I fill a cylindrical vessel with a gas and put a piston of some mass on top of it and slowly heat the vessel, the piston will move up. But does the pressure inside the vessel change? ( vessel is insulated).if pressure doesn't change, how does the piston move up? Pressure on piston : ##P -...
  22. AdityaDev

    Expansion of a Helium-Filled Balloon: Exploring Thermodynamic Processes

    If I heat a rubber balloon filled with helium slowly and if the balloon is fully expandable and (the balloon) can be assumed to require no energy in its expansion,what type of thermodynamic process is taking place? Is it isobaric? Since the balloon expands the pressure exerted by the gas on...
  23. M

    Isothermal Expansion of a Diatomic Gas

    Homework Statement A 0.300-kg sample of nitrogen gas (diatomic molecules,mN2 = 4.652 × 10^−26 kg) in a chamber fitted with a piston undergoes an isothermal expansion from 0.0500 m^3 to 0.150 m^3 . If the final pressure is 110 kPa, what is the final temperature? Homework Equations PV=N*kB*T...
  24. H

    Ring and Sphere Linear Expansion

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  25. ChristineMarie

    How to Calculate Entropy of an Ideal Gas During Expansion?

    How do you calculate the entropy of an ideal gas with n = 1, Cv,m = 1.5R, Ti = 300K, P=3bar and expands against Pext = 1bar until final volume is twice initial volume at Tf = 200K?
  26. G

    Fourier Series (Half-range expansion)

    Homework Statement Homework Equations The Attempt at a Solution I don't really understand why my solution is wrong as I think I have substituted everything in correctly.. Is it okay if anyone can help me take a look at my solution? Thank you. :) My solution: (Only bn) My...
  27. ezfzx

    Archived Linear temperature expansion - online calculator

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  28. V

    How to Apply Taylor Series at Infinity for x >> 1?

    Homework Statement How to use Taylor series for condition x>>1? For example f(x)=x\sqrt{1+x^2}(2x^2/3-1)+\ln{(x+\sqrt{1+x^2})} Homework EquationsThe Attempt at a Solution I try to derived it and limit to infinity...for example first term \frac{x^4}{3\sqrt{1+x^2}}. Limit this to infinity is...
  29. ckirmser

    A Mental Conundrum -- The Big Bang & the Speed of Light

    OK, knowing enough astrophysics to get myself hurt, I'd like to pose the following poser that whupped me upside the head while watching the Black Hole marathon last night on the Science Channel. We have; 1) The Big Bang theory, 2) An expanding - at least, for the moment - universe, and 3)...
  30. E

    Efficiently Calculate Binomial Expansion Coefficients | Homework Equations

    Homework Statement Consider the expansion (ax2 + bx + c)n = ∑(r=0 to r=2n) Ar xr------------------(1) , where Ar is real ∀ 0 ≤ r ≤ 2n Replacing x by c/(ax) and using the property ∑(r=0 to r=2n) Tr = ∑(r=0 to r=2n) T2n-r , we get (ax2 + bx + c)n = ∑(r=0 to r=2n) Br xr...
  31. L

    How Much Work Is Done in an Isothermal Expansion?

    I made a thread on this asking the general question in the other forum, but I don't know how to delete that thread. Homework Statement An isothermal expansion from Vi = 10.0 L, Pi = 2.46 atm against a constant external pressure until the Pf = 0.246 atm. How much work is done by the gas in...
  32. C

    Entropy in isothermal expansion

    Air: V1= 0,1 m3 P1= 1 MPa T1= 20 C After isothermal expansion P2= 0,1 MPa I had to find T2, M, V2, L, Q and found all those (T2=20 C; M=1,1927 kg; V2=1 m3; L=Q=230258 J) but need s (enthropy) for creating illustration in T-s I can`t find how it`s possible to calculate s1 and s2, is it possible...
  33. E

    Binomial expansion- divisibility

    Homework Statement The integer next to (√3 + 1 )^2n is -- (n is a natural number) Ans: Divisible by 2^(n+1) Homework EquationsThe Attempt at a Solution (√3 + 1 )^2n will have an integral and a fractional part. So, I + f = (√3 + 1 )^2n (√3 - 1 )^2n will always be fractional as (√3 - 1) < 1 So...
  34. Grinkle

    Plank length / space expansion question

    Do models of the expansion of space-time manifest that expansion by an increase in Plank-length, or by additional Plank-lengths appearing in between existing particles? I think it must be the latter because the Plank-length is not an empirically measured value and the constants it derives from...
  35. E

    Binomial Expansion Coefficient of x^n

    Homework Statement Find the coefficient of x^n in the expansion of ( 1 + x/1! + x^2/2! + x^3/3! + ... + x^n/n! )^2 . Homework EquationsThe Attempt at a Solution At first glance, this looks like the polynomial form of e^x, but the expansion of e^x goes to infinity, so any use of that seems...
  36. MexChemE

    Adiabatic expansion against constant pressure

    Homework Statement a) For a certain ideal gas CP = 8.58 cal mol-1 K-1. We have 2 moles of said gas at 293.15 K and 15 atm. Calculate the final volume and temperature when the gas expands adiabatically and reversibly until it reaches a pressure of 5 atm. (Answers: V = 7.45 L; T = 227.15 K) b)...
  37. A

    Could the Event Horizon of black holes be the edge of expanding universes?

    I recently read a few articles that contradict Einstein's Singularity theorem. The idea being that black holes are wormholes to other universes; with a white hole on the other side of the black hole (Poplawski's theory). What if instead of being a portal to another universe, the Event Horizon of...
  38. grandpa2390

    How do I use a taylor series expansion to find effective spring constant

    Homework Statement Let's pretend I am given a potential energy function and nothing else. I need to find the effective spring constant for oscillation about the equilibrium point using a taylor series expansion. I can't find an example or explanation anywhere on how to do this. the potential...
  39. N

    MHB Chebyshev Expansion (I understanding the provided solution)

    Hi, Please refer to attached image. I did an assignment earlier, and I got this question wrong. The solutions have been put up, but I struggle to understand how to proceed from $1*$ to $2*$ and also how the values for $T_4 = 8x^4-8x^2+1$ and $T_2 = 2x^2-1$ were derived. I would REALLY...
  40. aditya ver.2.0

    Question regarding to acceleration in the rate of expansion of our cosmos

    Dark Energy is one of the primitive forces of cosmos, existing since early years after Big Bang and its noted that its still is accelerating the rate of expansion of our universe. My question is that what is the source of this mysteries force?People stay that it existed ever in the universe.So...
  41. N

    Gravitation and Binomial Expansion

    Homework Statement Use the binomial expansion (1± x)n = 1± nx + (n(n-1)/2) x2 ±... to show that the value of g is altered by approximately Δg ≈ -2g(Δr/rE) at a height Δr above the Earth's surface, where rE is the radius of the Earth, as long as Δr<<rE Homework Equations g=GM/r2 The Attempt...
  42. evinda

    MHB What else could we do? (p-adic expansion)

    Hello! (Wave) I want to find the p-adic expansion of $\frac{1}{p}$ and $\frac{1}{p^r}$ in the field $\mathbb{Q}_p$. So, do I have to solve the congruences $px \equiv 1 \pmod {p^n}, p^r x \equiv 1 \pmod { p^n }, \forall n \in \mathbb{N} $, respectively? But.. these congruences do not have...
  43. Jonnnnn

    Someone me with this Laurent Expansion

    Homework Statement the Laurent expansion of f(z)=e1/sin(z) at the isolated singularity z=π Homework EquationsThe Attempt at a Solution I tried rewriting 1/sin(z) into exponential form, but it seems have no help for the expansion. Would someone give me some inspirations?
  44. F

    Ideal Gas Expansion - Finding final pressure and work done by gas

    Homework Statement a ideal monoatomic gas initally has a temperature of 315K and a pressure of 6.87atm . It then expands from a volume of 440cm^3 to volume 1550cm^3 . If the expansion is isothermal, what is (A) the final pressure (in atm's) and (B) the work done by he gas. Homework Equations...
  45. I

    Calculating Entropy Change in an expansion

    1. Suppose that you have a sample of a gas in a cylinder equipped with a piston that has a volume of 1.50 L, a pressure of 1.20 atm, and a temperature of 250 K. Suppose that the gas is expanded reversibility under isothermal conditions until the pressure is 0.75 atm. What is the entropy change...
  46. T

    Understanding an expansion into a geometric series

    Hi all, I am reading through Riley, Hobson, and Bence's Mathematical Methods for Phyisics and Engineering, and on page 854 of my edition they describe (I am replacing variables for ease of typing) "expanding 1/(a-z) in (z-z0)/(a-z0) as a geometric series 1/(a-z0)*Sum[((z-z0)/(a-z0))^n] for n...
  47. F

    Change in entropy, quasistatic, isothermal expansion

    Homework Statement I am to show that ΔS=Q/T for the isothermal expansion of a monoatomic ideal gas, when the expansion is so slow that the gas is always in equilibrium. Homework Equations 1. law: ΔU=Q+W (We mustn't use dQ and dW - our teacher hates that :( ). Ideal gas law: PV=NkT We need the...
  48. evinda

    MHB P-adic Expansion: Find $\frac{1}{2}$ in $\mathbb{Q}_3$

    Hi! (Wave) I want to write the $p-$ adic expansion of the number $\frac{1}{2}$ in the field $\mathbb{Q}_3$. How can I do this? (Thinking)
  49. B

    Laurent series expansion of Log(1+1/(z-1))

    Homework Statement Find the Laurent series expansion of f(z) = \log\left(1+\frac{1}{z-1}\right) in powers of \left(z-1\right). Homework Equations The function has a singularity at z = 1, and the nearest other singularity is at z = 0 (where the Log function diverges). So in theory there should...
  50. K

    Cosmological Expansion: Estimating Present Horizon Length

    Homework Statement If light traveled a distance L = H_{eq}^{-1} at M-R equality, how large does this distance expand to at present? (in Mpc) Homework Equations z_{eq} = 3500 \Omega_m = 0.32 at present \rho_c = 3.64 \times 10^{-47} GeV^4 present critical density The Attempt at a...
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