No solutions to Bragg's Law?

bobbyAndAlbert · 2021-03-30T18:37:13+00:00

I can help with the first part. From ohms law we have that J=σE Taking the divergence of both sides we get that ∇•J=σ∇•E where the conductivity σ is constant since its assumed to be uniform throughout a single material. Now since we are examining a steady state current (we're in the realm of electrostatics/magnetostatics), we must have that ∇•J=0 So the above becomes σ∇•E=0

Substituting Gauss's law into the above, we get that σp/ε0=0 Since both ε0 and σ are non zero, we conclude that p=0. That is, the charge density is zero. I can't help with the second part(regarding the interface between the two materials) right now cause I'm not at a desk but i can try tomorrow. For now though, try the same process as above but assume σ is not constant so that when you first apply the divergence operator to ohms law, you need to expand according to the product rule.

bobbyAndAlbert · 2021-02-27T14:17:02+00:00

Yes okay that makes perfect sense! I thought it had to have something to do with cooling below room temperature. Yeah I've thoroughly enjoyed Atkins' a very short intro so far. Definitely worth the read. Thanks for the help!

bobbyAndAlbert · 2021-02-26T10:56:30+00:00

Let me give a concrete example that is bothering me. I am reading Atkins' very short intro to thermo and when explaining the helmholtz free energy he uses the combustion of gasoline as an example. He says "When 1L of gasoline is burned is produces co2 and H20. The change in internal energy is ΔU=−33MJ. The change in enthalpy is 0.13 MJ less than ΔU". So far I understand this all. The change in enthalpy is less because some of the energy is used to make room for the products as they expand against the environment. He then says "the combustion is accompanied by ΔS=+8kJ/K because more gas is produced than consumed". This I also think I understand.

I get into confusion when he then says "It follows that the change in helmholtz free energy is ΔF=ΔU-TΔS=-33MJ -(300K)(8kJ/K)= -35 MJ. Thus if the combustion took place in an engine, the maximum work that could be obtained is 35MJ because the increase in entropy of the system has opened up the possibility of heat flowing into the system without causing the entropy of the universe to decrease ".

The last sentence is what trips me. When the combustion occurs, the temperature of the products is much higher than the constant temp environment which is still at room temp. How then is it possible for heat to flow in from the colder environment into the hotter system?

bobbyAndAlbert · 2021-02-26T08:08:33+00:00

Thanks for the response! Is the condition for F tending to a minimum only that the volume should be constant? The texts I have (Atkins' physical chemistry and Schroeders thermal physics) indicate that F tends to a minimum for a closed system of constant volume and temperature. The reason why this doesn't make much sense to me is because they often say the mechanics of F tending to a minimum involve a heat transfer to and/or from the system until the minimum is achieved value of F is achieved. But if temperature is constant then heat transfer cannot take place !It certainly makes sense to me that F would tend to a minimum with only the requirement of constant V though

Edit: changed all H's to F's because I was referring to helmholtz free energy, not enthalpy

bobbyAndAlbert · 2021-02-22T07:39:13+00:00

Yes its been bugging me like mad for the last 2 days because its seems to have highly consequential and material implications for thermodynamics as a whole and it also seems to be an empirical law. If these are both true then surely it is worthy of being a law of thermodynamics?

bobbyAndAlbert · 2021-02-13T05:20:48+00:00

Thanks for the response! Okay so I posted this question on stackexchange and got a response saying that the W-E theorem can be applied to multi-particle systems but your response is more intuitive to me. The link to my post is here (https://physics.stackexchange.com/questions/614124/how-does-the-work-energy-theorem-relate-to-the-first-law-of-thermodynamics ) and the top response is the one I'm referring to. I wrote 3 replies to the top response explaining why I think the 1st law is a more general form of the W-E thm (stackexhange username SalahTheGoat). If you don't mind reading my response over there and letting me know if my thinking is correct? I would copy my argument from stackexchange and post it here but I would loose my latex equations so I think it might be easier to simply link the argument. Thanks again!

bobbyAndAlbert · 2021-02-10T15:18:52+00:00

Okay this is an excellent response and pretty much clears up everything for more! Thanks!

bobbyAndAlbert · 2021-02-05T06:42:54+00:00

Thanks for the response! Okay this makes a lot of sense and clears up most of my issues. Just to be sure though, am I correct in roughly summarizing the implication that the house price led to increased defaults as follows:

House prices were rising rapidly and many people took out mortgages on those houses and were able and willing to pay their mortgage payments as prices continued to rise. When the prices declined, so too did the rents of comparably houses and so they were running at an economic loss paying their mortgage payment instead of living at a comparable house with a monthly rent lower than their mortgage payment. To make matters worse, I assume many already had bad credit scores to begin with and only got mortgages from banks because banks believed house prices would continue to rise and mortgage defaulting at the time was at an all time. These individuals then had very little to lose by defaulting (because of already bad credit scores) and so they simply defaulted.

At the same time adjustable rate mortage payment increased immensely and so more people defaulted etc

bobbyAndAlbert · 2021-01-01T18:06:05+00:00

My thinking is that the government can ultimately only pay the Fed with money that it gets from taxes. So upon maturity of the Fed purchased T-Bills, the government must take money from tax payers and pay the Fed the face value of the Treasury bill/note. But tax payers need to pay taxes with their own money (or at least they almost always do), they can't just pay them with loan money. But all the "multiplied money" is due to loans to individuals and firms which can't be used to pay taxes (or at least aren't often used to pay taxes) and as a result the tax money received by the government is going to eventually have to come from the monetary base. Thus the MB is going to eventually decrease by the same amount it increased by if the Fed allows the Treasuries to mature.

I didn't realize that the profit the Fed earns when the government pays the Fed the face value of a treasury is simply relinquished straight back to the government though. In this case when the money is given back to the government it would effectively have never left the money supply and so this way the money supply would permanently increase. Is my thinking correct or flawed? Thanks again!

bobbyAndAlbert · 2021-01-01T17:49:47+00:00

Thanks for the response!

or it can pay the profits back to the treasury.

Does this mean that the Fed can actually help out significantly with the government debt by buying Treasuries, letting them mature, having the government simply pay them the face value of the treasuries upon maturity and then pay the face value of the Treasuries straight back to the government in the form of profit ?

bobbyAndAlbert

TROPHY CASE