Recent content by Ron19932017

Thank you for your reply! I checked again Euler's equation writes U=-PV+TS+##\mu## N, previously I missed the chemical potential term, it turns out that in the case of free expansion of V->2V, although ##\Delta## (-PV)=0, while ##\Delta (TS)=nrT ln(2)##, the chemical potential decreases...

The equation U=-PV+TS is called Euler's equation, and is derived from the homogenous property of extensive variables. Start with a chamber of gas with a state of (P,V,T), consider the first law of thermodynamics, dU=-PdV+TdS, when we homogeneously increase volume and entropy (extensive...

Hi everyone, I am confused when I apply Euler's equation on the free expansion of an ideal gas. Consider a free expansion (expansion of gas in vaccum) where the volume is doubled (V->2V) The classical free expansion of an ideal gas results in increase in entropy by an amount of nR ln(2), a...

Thanks for your reply. If we put gases directly on the surface of the Sun we increases the Sun's pressure so it will be hotter. However I think we can still just imagine a situation that, the surface shell is departed from the fusion core, like the gas sit in a shell-shaped container and are...

Yes, you are right. Our Sun is not blackbody-like in the fusion site, but it is blackbody like at the surface. Maybe I should address the question like this: How can we modify the photosphere to make it a better blackbody? Can we do it by increasing the density, and why?

I wonder how an object, like our sun, can approach a more perfect blackbody. We know that by the wiki definition, blackbody is something that absorb all radiation and is in thermal equilibrium. Its spectrum only depends on T. We also know that, our Sun's spectrum is blackbody like, while a...

If the x-momentum is flowing in at surface ##x## and flowing out at surface ##x+dx##, then there will be energy flowing in and out through these two surfaces too. The two energy flow balances each other and results in no change in energy density in the interval ##(x,x+dx)##. Why does the stress...

Consider an interval ##(x,x+dx)## in a 1-D tube of fluid in equilibrium. In your picture do you mean there is a momentum flux flow in at surface ##x##, meanwhile there is a flow out at surface ##x+dx##. Or do you mean at any surface (say ##x##), there is both a flow in and flow out such that net...

If the net momentum flux is zero, why do we write ##T^{1,1}= P##, but not zero? For example an observer placing a plate in ##dx## orientation in a tank of perfect fluid will agree that momentum density flux measured is zero. I think it is natural to claim ##T^{1,1}=0##.

Hi all, I am reading Bernard Schutz's a first course in general relativity. In Chapter 4 it introduced the energy stress tensor in two ways: 1.) Dust grain 2.) Perfect fluid. The book defined the energy stress tensor for dust grain to be ## p⊗N ##, where ##p## is the 4 momentum for a single...

Hi everyone, I am reading Sean Carroll's note on gr and he mentioned metric compatibility. When ∇g=0 we say the metric is compatible. However from another online material, the lecturer argues ∇ of a tensor is still a tensor, and given that ∇g vanish in locally flat coordinate and this is a...

I see. Sorry I have a few more questions. 1. The logic is like : Exterior derivatives are p-forms -> df is the exterior derivative of a scalar function -> df is a 1 form? 2. How can we make sure exterior derivative are a (0,p) tensor at the beginning? 3. Which way we do formally testify...

Thank you for you reply. I understand ##df## is a map from tangent vector to real number by ##df(X) = X^\mu \partial_\mu f## and how you get the ##d x^\mu## as 1-form basis. 1.)However how can you make sure all ##df## can be expressed in linear combination of ##d x^\mu##? My intuition tells...

Hi everyone I am reading Sean Carrol's lecture notes on general relativity. link to lecture : https://arxiv.org/abs/gr-qc/9712019 In his lecture he introduced dxμ as the coordinate basis of 1 form and ∂μ as the basis of vectors. I understand why ∂μ could be the basis of the vectors but not for...

How can I really identify a space eg the phase space is not Euclidean? I remember in the example of Fermi-degenerate gas, or some other model we are counting the state density in the reciprocal space/momentum space, it looks like the momentum space is Euclidean because all axis are orthogonal...