Expansion Definition and 1000 Threads

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?

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...

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...

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...

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...

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?

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...

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...

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...

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:

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)

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?

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...

Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...

I have to do a Taylor expansion of the energy levels of Dirac's equation with a coulombian potential in orders of (αZ/n)^2 , but the derivatives I get are just too large, I guess there is another approach maybe? This is the expression of the energy levels And i know it has to end like this:

Consider the integral $$ G(x) = \int_0^\infty \frac{e^{-xt}}{1+t}dt$$ which is convergent for x>0. For large x, it is dominated by small t so expand: $$G(x) = \int_0^\infty e^{-xt}\sum_{m=0}^{\infty}(-t)^mdt$$ From here my notes say to take out the summation and write: $$G(x) =...

Homework Statement 2kgs (total mass) of steam goes through a revesible isothermal expansion at 500 degrees celcius. During the expansion the pressure drops from 300 kpa to 200 kpa. What is the heat absorbed by the steam during this process? Homework Equations U=W and W=nrt ln(v2/v1) The...

Hi, my question is related to taylor expansion of metric tensor, and I have some troubles, I would like to really know that why the RED BOX in my attachment has g_ij (t*x) instead of g_ij(x) ? I really would like to learn the logic...

Hi all, Given: I have a pressure vessel of 1000M^3 filled with water with 8 bar pressure. On this pressure vessel I have installed a valve and a expansion vessel on top of the pressure vessel. The expansion vessel is prepressurized to 8 bar as well. Question: when I open the valve i lose 20...

Homework Statement The question is: What happened with the entropy in a free expansion? The system is isolated and the state equation is: $$p=AT/V+B/V^2$$ Homework Equations $$dU=TdS-pdV$$ The Attempt at a Solution My attempt is: Because the system is isolated and corresponding to an free...

Hello, I may working through attached paper and really need help with deriving equation in appendix - A4 to give A10. http://iopscience.iop.org/article/10.1088/0004-637X/744/2/182/pdf Any help would be greatly appreciated. thanks, Sinéad

<Moderator's note: Moved from a technical forum and therefore no template.> Hey All, For my modern physics class we were told to write out a binomial expansion of (1+(1/x))^(-3/2). I am fairly confident in the work I did, but my professor posted his work and it is different and way simpler...

Is there any theory to say if expansion started with a finite seed and propagated out at a finite speed vs somehow happening everywhere at once? I know the layman's phrasing is that expansion happened everywhere at the same time. That might just mean that the very small part of the early...

Hi, I really wonder how these second derivatives can be written in terms of christofflel symbols. I have made so many search but could not find on internet What is the derivation of equations related to second derivatives in attachment?

Hi, I would like to express that r and r' are vectors in the attachment and let's say that r is observer distance vector r' is source distance vector. By the way I know this is taylor expansion (for instance if there was only x component (scalar form) I would not any ask question ). But I do...

How do you tell the difference of expanding outwards and contracting inwards? Part of my intuition tells me that it would be impossible to tell the difference. If you are on the natural numbers heading from zero to infinity I might say that is expanding outwards. So if you are sitting at...

One thing that has always puzzled me is that the farther we look out into the universe we see that galaxies are moving away from us faster than galaxies that are closer to us, but also the farther we look out into space the farther back in time we are observing. I have trouble understanding...

hello there, I am totally into all astrophysics. so I want to know, how fast is the known universe at the most outer edge moving? or in other words, how fast is the most outer edge expanding away from earth. - and what's the rate of acceleration? I mean even if, as I understand it, the space...

When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...

I am trying to understand something. Let me pitch a scenario: You have two asteroids in a vacuum. Each is large enough to be round by gravity. They are separated by roughly the distance from the Earth to the moon. Relative to each other, they are moving at 0 in all directions (aka, they are...

Could anyone please guide me how to do these problems?

Homework Statement Assume that one mole of an ideal van der Waals fluid is expanded isothermally, at temperature T_h from an initial volume V_i to a final volume V_f. A thermal reselvoir at temperature T_c is available. Apply dW_{RWS} = \left ( 1 - \frac{T_{RHS}}{T} \right ) (-dQ) +(-dW) to a...

Something that routinely comes up as a problem at work is when we size flow projects for piping systems. We calculate pressure drop across a length of fixed diameter for compressible gasses, but we do not calculate pressure changes through an expansion or contraction with gas (for example...

Homework Statement Find the Maclaurin series and inverval of convergence for ##f(x) = \log (\cos x)## Homework EquationsThe Attempt at a Solution I used the fact that ##\log (\cos x) = \log (1+ (\cos x - 1))##, and the standard expansions for ##\cos x## and ##\log (x+1)## to get that...

Consider two bodies A &B are moving apart with a velocity V due to the expansion of space. According to an observer in A the body B is moving away and an observer in B feels the body A is moving apart. Can some one answer in which body the time dilates and why?. ( I am specifying once again that...

So in the book it says expend function ƒ in ε to get following. ƒ=√ (1 + (α + βε)2) = √ (1 + α2) + (αβε)/√ (1 + α2) + (β2ε2)/2 (1 + α2)3/2 + O(e3) When I expend I get(keeping ε = 0) ƒ(0) = √ (1 + α2) -->first term ƒ'(0) = (αβ)/√ (1 + α2) --> sec term with gets multiplied by ε for third...

Homework Statement An ordinary glass is filled to the brim with water at 100oc. How much water could be added to the glass if the temperature is lowered to 20oC? Assume that the coefficient of volume expansion for glass is 2.7 x 10-5 K-1 and for water it is 2.1 x 10-4 K-1.Homework Equations ΔV...

If my professor tasked me with finding out where to find the materials for setting up an electromagnetic ring expansion test, where is a good place to start? Generally, what is a good procedure to follow when setting up an experiment? I am not very experienced but I would like to learn. The...

As I understand it, in the context of cosmological perturbation theory, one expands the metric tensor around a background metric (in this case Minkowski spacetime) as $$g_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$$ where ##h_{\mu\nu}## is a metric tensor and ##\kappa <<1##. My question is, how...

It is been said that the universe is expanding but the question is,where will the universe end? Are we the only universe?

Neutrinos were flavor eigenstates at the time of their decoupling from baryonic matter. Since they were not pure mass eigenstates, how do you take this fact into account if you try to study how they evolved as the universe expanded? Could we determine if the heaviest neutrino could be non...

Okay, I will give a quick run down of what I am trying to do here. What I want to do is build a tesla turbine from old hard drive disks. Being that they're already rated for high RPM, it seems like a viable option. Now these disks are probably going to be aluminum and I am probably going to buy...

Hello ! I have troube doing a calculation. Let's say we have a volume Vi in a tank at a pressure Pi. If I let my tank open, the tank's liquid will start to boil to keep the pressure Pi inside the tank. Now, at the end, I will have a volume Vf in the tank, and still a pressure Pi. But the...

PLEASE BE ADVISED: I'm a complete ignorant with regards to the details of what I'm about to say and I've never looked at the mathematics of the subject, let alone understand it. So most of what I am about to say comes from pop science. Excuse me in advance if I sound stupid or rhetorical...

Homework Statement http://i.imgur.com/swYr8aw.jpg Homework Equations delta L=LalphadeltaT The Attempt at a Solution sorry for s**ty handwriting look at #8[/B] http://i.imgur.com/59Ew8vJ.jpg edit:click the links please. The forum software cropped the quality of the photo.

Light can get red-shifted due to expansion of space, this leads to a loss of energy. Would it be possible that this energy is what's causing the universe to expand in the first place?

In his book Gravitation and cosmology, Weinberg derives the perihelion precession of Mercury in the Robertson expansion. The final formula is \Delta\phi =\frac{6\pi M G}{L} \frac{2+2\gamma-\beta}{3} The second term is one for GR (β=γ=1). I have two questions regarding this formula: 1. The...

Hello, I have some trouble understanding the virial expansion of the ideal gas. 1. Homework Statement I have given the state equation: $$ pV = N k_b T \left(1+\frac{A\left(T\right)}{V}\right) $$Homework Equations [/B] and a hint how to calculate the caloric equation of state $$...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] Hi, I am trying to understand the 2nd equality . I thought perhaps it is an expansion of ##(1-\frac{z}{w})^{-2}## (and then the ##1## cancels with the ##1## in ##( (1-\frac{z}{w})^{-2}) -1 ) ##) in the form ##(1-x)^{-2}##...

Homework Statement A one-liter pot is completely filled with oil. Heat is applied to the pot&oil and the temperature rises from 15°C to 190°C. How much oil is spilled over? The linear coefficient of thermal expansion for oil is 0.68*10-3; the one for the pot is 2.4*10-5 Homework Equations...