Expansion Definition and 1000 Threads

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...

Hi, The coefficient of thermal expansion for aluminium is 23ppm/C at 20C = 0.000023m per degree in temperature (C). Is this temperature: (1) the temperature of the air circulating around the material in the sun, (2) the temperature in the shade at that time of the day, or (3) the tactile...

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...

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...

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 |##...

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...

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...

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...

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...

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...

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

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...

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...

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...

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 -...

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...

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...

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...

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?

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...

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...

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)...

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...

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...

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...

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...

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...

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...

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)...

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...

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...

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...

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...

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...

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?

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...

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...

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...

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...

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)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...