Expansion Definition and 1000 Threads

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...

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...

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}}...

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...

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...

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...

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}...

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...

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...

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?

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?

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...

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...

Space evidently is expanding, so we say that the very fabric of space time is expanding uniformly in all directions, so two questions 1)originally this expansion was driven by the energy content within the universe aka the dense hot matter , versus nowdays the acceleration is picking up speed...

I hope that I am conveying what I see in my head clearly. I guess that I am visually imagining the 3 spatial dimensions projected on the 2d surface of a sphere and as that sphere expands that the increased distance between 2 points would happen what seems like at an accelerating rate because of...

Let's say I have a liter of gas at pressure of 4 atm and T=900K. I use it to move perfect massless frictionless and insulative piston to compress a liter of 1 atm, T=300K gas. When the pressure on both sides is equal and the piston stops moving, will the temperature on both sides of the piston...

I am trying to find out where to get the Thermal coefficient of expansion for glycerin. The only thing I keep getting when using Google is mathematical examples that use glycerin as an example and its coefficient but I need to know where this number is coming from. Ex: 4.85 × 10^-4 (°C)-1

##\Delta V = \beta V \Delta T####\rho _2 = \frac m {V + \Delta V} = \frac { \rho V} {V(1+\beta \Delta T)} = \frac \rho {1+\beta \Delta T}## ##\Delta \rho = \rho _2 - \rho = \frac \rho {1+\beta \Delta T} - \rho = \rho (\frac 1 {1+\beta \Delta T} - 1) = \rho \frac {-\beta \Delta T} {1+\beta \Delta...

I get $$B_2(T)=2\pi N\int_{0}^{\infty} (1-e^{-\beta E_0((\frac{r_0}{r})^{12}-2(\frac{r_0}{r})^6)})r^2dr$$ as the coefficient. I was just unsure how to evaluate it numerically from here. Any suggestions would be appreciated. Thank you.

Does the CMBR contain the imprint of the entire expansion history of the universe or only of the last scattering ?

Homework Statement: Use Taylor expansion to show that for ##u \in C^4([0,1]) ## $$ max |\partial^+\partial^-u(x) - u''(x)| = \mathcal{O}(h^2)$$ For ##x \in [0,1]## and where the second order derivative ##u''## can be approximated by the central difference operator defined by...

I do not understand how this formula is derived: Can somebody help me? Source: https://www.corzan.com/en-us/piping-systems/specification/thermal-expansion

Summary: Is it possible to tell the current average universe expansion rate i.e. acceleration of expansion in m/s^2 ? Is it possible to tell the current average universe expansion rate i.e. acceleration of expansion in m/s^2 ? If i say in relation to earth, does this make it easier to answer...

I am searching for the appropriate methodology/equation(s) to step beyond Boyle's Law to account for the phase change and solve this problem. All suggestions/guidance is greatly appreciated! Bruce

Part (a) ΔS = ∫ (dq/T) because: dq = PdV = (nRT/V)dV Then: ΔS = ∫ (1/T)*(nRT/V)dV ΔS = nR ∫(1/V) dV ΔS =nR[ln(V2/V1)] Part (b) This is where I'm stuck. I know [P + a/(v/n)2][v/n - b] = RT can be solved for P and simplified to P = [RT/(v-b)]-[a/v2] since n=1mol But I don't know how to proceed...

Summary: Can someone give me a basic high level overview on how to do a binomial expansion? I'm studying for my E&M test and going over multipole expansion. I'm particularly confused about these lines (Griffiths E&M 4th Edition) 𝓇^2_{\pm} = r^2 \left(1\mp \frac{d}{r} \cos\theta +...

As titled, been cracking my head over it. Thanks in advance!

for the case, r>>r' the higher-order term like 1/r^2 and above that is negligible. so V(r)=cons.*1/r*P0(cos a) but for the case r'>>r will it be V(r)=cons.*1/r'[ summation Pn(cos a')t'^n] where t'=r/r' now if we neglect higher-order term of r/r' then V(r)=cons.*1/r'*P0(cos a') which is...

Hi everyone, I'm interested in relativistic anisotropic hydrodynamics and often a "gradient Expansion" is mentioned in articles, but not how this works exactly. I gathered that this is some kind of expansion of the energy-momentum tensor. Can someone explain to me how this expansion is set up...

Summary: The universe is expanding, so at one point in the past it must have been all concentrated into a single point. But is this really an accurate observation? Hi, This is my second probably naive question that's been on my mind as a lay-scientist for a long time (the other will hopefully...

This is a repost as I didn't read the community guidelines the first time. Hopefully this is better! First thing I did was write down both the linear and volume expansion formulas. I then multiplied my alpha by 3 and used the volume expansion equation for both materials. ∆V oil > ∆V pot, at the...

Summary: Help with volume and length expansion question Hi, I am struggling with this question. I understand that beta = 3 alpha so you use this to sub into the volume expansion equation. Is this correct? Can someone please provide a step by step instruction on how to do this question? Thank you !

The rates I've come across are 67, 71 and 74. Obviously it's not 74 as it was just announced. Is it one of these other numbers, something else? I'm only asking out of curiosity.

Suppose light travels during a time interval of t2 - t1, where the scale factors at t1 and t2 are a(t1) and a(t2) respectively. If we consider an infinitesimally small interval of time dt during this interval, without accounting for expansion we would expect light to travel a distance cdt. How...

A basic question... The further a galaxy is from ours, the more redshift, the faster it is moving away from us. This is taken as a sign the universe is expanding at ever increasing rate. Yet... As we look farther out into space, we are also looking back in time. If the farther we look back in...

Disclaimer: I am parroting the information in this from articles that I've read. This post is to try to get a better understanding of what they are talking about and if any of it is relevant. I came across an article regarding the Big Bang while looking into the current rate of universe...

In the process of developing a tank venting program and starting to investigate how to incorporate tank gas expansion cooling I realized that since: T=P/nR with R constant and the reduction of P and n directly proportional then this equation implies all tank ventings are isothermal. What am I...

Given that the expansion takes place "in nothing". Given that all space-time exists all of the time. (past/present/future) If the ultimate fate of the Universe is that it collapses back in upon itself. Shouldn't a singularity of space-time occur instantaneously? After all, all time existed...

Recently I was thinking about the Hubble's constant (which, actually, is not Hubble's and not constant...) and wondering: if the universe is expanding at 70 km/s each Mpc, then there's possible to calculate some expansion of space, say from me to a person 1 meter away from me (theoretically)...

So I'm on page 67 of Marion/Thornton's "Classical Dynamics of Particles and Systems" and I'm in need of some help. I understand that so far there's is an equation that cannot be solved analytically (regarding motion due to the air resistance and finding the range of the an object shot from a...

I have been playing around with Taylor expansion to see if I can get anything out but nothing is jumping out at me. So any hints, suggestions and preferably explanations would be greatly appreciated as I’ve spent so so long messing around with it and I need to move on... But as always, thank you

Hello everyone. I am currently using the pca function from MATLAB on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...

Summary: Expansion of matter in the visible universe, total volume of space outside the visible universe, black hole mechanics, and general questions from an uneducated but extremely interested evolved monkey. Hello everyone! I do not know the rules of this forum, or any forum for that matter...

I expanded the exponential with the derivative to get: ## Z = \Bigg(1 + \frac{1}{2} \frac{\partial}{\partial x_{i}} A^{-1}_{ij} \frac{\partial}{\partial x_{j}} + \frac{1}{4} \frac{\partial}{\partial x_{i}} A^{-1}_{ij} \frac{\partial}{\partial x_{j}} \frac{\partial}{\partial x_{k}} A^{-1}_{kl}...

As indicated in the title and summary, I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship, by measuring individual galaxy subtended angles over time. The...

I tried diffrentiating upto certain higher orders but didn’t find any way.. is there a trick or a transformation involved to make this task less hectic? Pls help

So the universe is expanding, and galaxies are getting farther apart from one another on average. Does this motion count the same as ordinary motion, in that if a galaxy is being expanded away from us at 0.5c, that clocks in that galaxy would appear to tick slower at 0.866 the rate of clocks here?

As I said before, I really have no idea on how to proceed.

I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2. There's a great example in wikipedia which is almost...

Space/time is relative. What is the expansion relative to? Is there a reference point of no expansion to make a comparison? Accelerated contraction would appear to be expansion by an observer looking back in time so how can we be certain that the universe is expanding instead of collapsing at...