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. 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 |##...
  2. 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...
  3. 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...
  4. M

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

    Homework Statement Give the first three terms and the general term for ((e^x)-1)/xHomework Equations None The Attempt at a Solution[/B] I wasn't sure if I would be able to take the e^x series and subtract 1 from each term and divide each term by x. I was also thinking of splitting it into...
  5. 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...
  6. 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...
  7. 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
  8. 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...
  9. 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...
  10. 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...
  11. 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 -...
  12. 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...
  13. 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...
  14. H

    Ring and Sphere Linear Expansion

    Homework Statement A 25.0 g copper ring at 0°C has an inner diameter of D = 2.71585 cm. A hollow aluminum sphere at 88.0°C has a diameter of d = 2.72019 cm. The sphere is placed on top of the ring (see the figure), and the two are allowed to come to thermal equilibrium, with no heat lost to the...
  15. ChristineMarie

    Calculating entropy for 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?
  16. 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...
  17. ezfzx

    Archived Linear temperature expansion - online calculator

    Here's a cool online thermal expansion calculator. It's OK and might even lead to other interesting websites. http://www.engineeringtoolbox.com/linear-thermal-expansion-d_1379.html
  18. V

    Taylor expansion in infinity?

    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...
  19. 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)...
  20. 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...
  21. L

    Work of 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...
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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)...
  27. 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...
  28. 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...
  29. 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...
  30. 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...
  31. 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...
  32. 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...
  33. 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?
  34. 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...
  35. 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...
  36. 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...
  37. 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...
  38. 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)
  39. 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...
  40. 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...
  41. I

    Relativistic mechanics Taylor expansion

    Homework Statement For a particle traveling near the speed of light, find the first non-vanishing term in the expansion of the relative difference between the speed of the particle and the speed of light, (c-v)/c, in the limit of very large momentum p>>mc. Hint: Use (mc/p) as a small parameter...
  42. R

    Sinking instead of expanding universe?

    We all know the concept of the universe expanding. Would it be possible that the universe is not expanding at all, but the spacetime between objects is increasing? My question comes from the idea that spacetime is changed due to the presence of gravitational objects and the idea that gravity is...
  43. E

    Multipole expansion - small problem

    Homework Statement Jackson 4.7 Given a localized charge distribution: \rho(r)=\frac{1}{64\pi}r^{2} e^{-r} sin^{2}\theta make the multipole expansion of the potential due to this charge distribution and determine all nonvanishing moments. Write down the potential at large distances as a...
  44. Flutterguy123

    What is the rate of gas expansion in a vacuum?

    Say that there's a large metal box with nothing but a vacuum inside of it, except for a small bag of compressed gas at the center. If the bag were to suddenly pop, is there a specific rate that this gas would accelerate when expanding to meet the space of the container? I think that it might...
  45. skate_nerd

    MHB Does this problem warrant a taylor expansion? (solid state physics)

    The whole problem I'm doing here is not even really relevant, so I won't go too much into it...I'm told to find an atomic form factor given some certain conditions, and I do a big gross integral and got this: $$f=(\frac{4}{4+(a_oG)^2})^2$$ where \(a_o\) is the Bohr radius and \(G\) is the...
  46. K

    Solving expansion rate for a variant of the Friedmann equation

    Homework Statement For the equation H^2 = \frac{8 \pi G \rho_m}{3} + \frac{H}{r_c} how do I find the value of H for scale factor a \rightarrow \infty , and show that H acts as though dominated by \Lambda (cosmological constant) ? Homework Equations \rho_m \propto \frac{1}{a^3} H > 0...
  47. Z

    Understanding Expansion of Space

    So what I don't get about the expansion of space, and what I'm assuming one of you can explain to me, is that it seems like if space were expanding, how would we have any way of noticing it? It seems like as the distances between particles expands, so must the size of the particles themselves...
  48. A

    Why D? Exploring Isothermal Expansion

    Homework Statement http://puu.sh/c09sc/b1d02302bd.png Homework Equations Conceptual question. The Attempt at a Solution The answer is isothermal expansion(D). but heat does not decrease due to isothermal process and expansion leads to lesser collision of particles on walls of container. So...
  49. A

    Prove: Binomial Expansion for e^{2x}-1/e^{2x}+1 up to x^5

    Homework Statement Prove that, if x is so small that x^6 and higher powers of x may be neglected, then \frac{e^{2x}-1}{e^{2x}+1}\approx x-\frac{x^3}{3}+\frac{2x^5}{15} Homework EquationsThe Attempt at a Solution [/B] \\...
  50. G

    Plane wave expansion of massive vector boson

    I'm trying to derive Feynman rules for massive vector boson and its antiparticle. It all boils down to plane wave expansion of the bosons which atm is a little bit confusing. Should I account for two different set of ladder operators (as in the case of complex KG or spinors, cf Peskin&Schröder...
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