1

Chemistry / Re: How can I find the optimum ΔH and ΔS for passive T control?

« on: 25/05/2022 23:55:43 »

Hi.

This question is inspired

   Well, it is quite a good idea.

ΔG = –RTln([Z]/[A])

    Could you clarify this please?   I'm not sure what your ΔG is,  is it actually ΔG° ?   Are  [Z] and [A] concentrations at equillibirum only?   i.d.k.

This is the conventional equation:
    ΔG =   RT   Ln (Q/K) 
Where ΔG = Gibbs free energy change for the system, (in the forward direction and at the specified concentrations).
Q = quotient of concentrations of products / reactants =  [Z] / [A]
K = chemical equilibrium constant =  Quotient as above but AT EQUILIBRIUM.
   
    Just to clarify this,  this ΔG is a function of 3 variables:   The temperature, T,  and the concentrations [Z] and [A].

[reference:  https://chem.libretexts.org/Courses/Grand_Rapids_Community_College/CHM_120_-_Survey_of_General_Chemistry/7%3A_Equilibrium_and_Thermodynamics/7.11%3A_Gibbs_Free_Energy_and_Equilibrium ]

   There seems to be a K missing in your expression,    much as if you were assuming K always = 1.   
This could be enough to stop your idea working completely.    If  K = 1 always, then the net reaction never shifts forward or backward -  the equillibrium point remains with equal concentrations of products and reactants [Z] = [A]  regardless of what happens.   In this way it won't respond to changes in temperature at all.   
    To re-phrase this  K ≠1.  It is essential that K = K(T) = some function of temperature.

     Using conventional theory,   it seems that we can approximate  K(T) = equillibrium constant at temperature T  as
K(T)     ≈   e ^{-(ΔG°/ RT )}

    This quantity, ΔG°  is not a function of the concentrations of the products and reactants.   At most it is a function of the temperature, T, but more usually the temperature and pressure are also assumed to be standard temp. and pressure.   Since you're interested in changes occurring around room temp. and pressure, it shouldn't be a problem to assume  ΔG°  is just a constant  which you can find in a book for the reaction A → Z.

   Anyway, re-arranging that equation we obtain:   ΔG°  = -RT Ln (K)  =   -RT Ln ([Z]/[A])     where  [Z] and [A] are now only to be taken as the concentrations at equillibrium.     That might have been the equation you were suggesting in your original post.  It matters a lot because, if that was what you were doing,  then when you re-arranged it to find ΔH  I don't think it was the ΔH that you were actually hoping or thinking you'd find.

   Summary:  Sorry that was confusing.  I'm confused and just trying to match up your notation with that used in some other texts on the subject.  I need you to check or explain what it was you were hoping to suggest with your formula  ΔG = -RT Ln ([Z] / [A])  . 

Best Wishes.

2

Physiology & Medicine / Re: why is my skin so sensitive when I have a fever?

« on: 19/05/2022 16:14:22 »

Is this a known effect?

Very much so, especially for flu. It is similar to heightened sensitivity to sound and light, especially when feverish.

Is there a known (or likely) mechanism?
Is there anything I can do to limit it while recovering?

Apparently staying hydrated is a good way to limit it. Ibuprofen helps reduce inflamatory related symptoms, including the skin sensitivity. I found that acetaminophen does a nice job on headaches and fever, but not so helpful with the inflamation.

Benefit of covid: Our altered social practices have seemingly prevented about two years of all the common stuff I/we usually contract each year. Sorry this hasn't been entirely true for you.

3

General Science / Re: Is 2 really prime? If so, why isn't 1?

« on: 01/05/2022 04:11:50 »

There are also prime polynomials (if you ignore imaginary zeroes).
- These are important in telecommunications and encryption schemes

[Spoiler:]

4

General Science / Re: Is 2 really prime? If so, why isn't 1?

« on: 30/04/2022 00:19:02 »

Hi.

I came across another wrinkle: what about –1?

    Your general arguments after this are reasonable.   However, I think it is again just a matter of simplicity and having a set of numbers that are useful for something.   It is possible and useful to confine your attention to what people might call the counting numbers or the Natural Numbers, so we do.   That doesn't mean that mathematicians have never considered generalising the idea of prime numbers and investigating properties like prime factorisation in a structure bigger or more abstract than just the positive counting numbers - they certainly have.

   There is already some terminology you could use to describe a set of things that behave like prime numbers but apply to a much more generalised set of objects than just the Natural numbers.   These things are called "prime elements" and the parent algebraic structure is known as a "Ring".   You seem to be interested in the Ring which is the Integers (positive and negative Naturals with 0,  under  conventional binary operations of + and x).

   See   Wikipedia entry:   Prime elements, if you're interested.   https://en.wikipedia.org/wiki/Prime_element
However, you should note that they exclude "units" which would  include -1  in the ring of Integers,   i.e.   they would directly exclude both  +1  or  -1   from the prime elements in the ring of Integers.  (For what reason?   Similar to excluding 1 from the primes,  it makes it much easier to state an equivalent unique factorisation theorem for the ring of Integers).

    Here's a quick question or puzzle, just for fun.   It relates to the idea you mentioned earlier of eliminating the number 2 from the prime numbers.   You also seemed keen to extend beyond the positive numbers and consider negative numbers but you really don't have to stop there - you can consider Complex integers.
    The Complex Integers or "Gaussian Integers"   are the  Complex number equivalents of integers.   Specifically, the Gaussian integers are the set of all complex numbers of the form   a+bi   where  a and b are integers.
    Just like in ordinary arithmetic with Natural numbers, a prime  (or prime element) of the Gaussian integers is a Gaussian integer,  p,  that is irreducible or cannot be factorised.   Specifically,   if we have  p =  q × r   (where × is just ordinary multiplication of the complex integers q and r)  then  at least one of  q or r must be a unit element.     A  "unit"  is any complex number that lies on a unit circle around 0,  so the only  units in the  Gaussian integers are    +1, -1,  +i, -i.
   The number 2   is a prime in the ordinary integers.   Is it still a prime in the Gaussian integers?   To say that another way, can you factorise the number 2 in the Gaussian integers?

Spoiler: show

  2  =   (1+i) (1-i)   = the product of two Gaussian integers, neither of which are unit elements.   So 2 is not prime in the Gaussian integers.
  As it happens, the Gaussian integers do form a Unique Factorisation Domain.   This means there is a set of prime elements often called Gaussian Primes, all the Gaussian integers can be written as a product of those prime elements and, as always, that factorisation is unique.   However, its prime elements are quite different to the prime numbers of the ordinary Integers.

Best Wishes.

[Spoiler:]

5

General Science / Re: Is 2 really prime? If so, why isn't 1?

« on: 28/04/2022 18:22:32 »

Hi.    Fantastic diagrams.   Great that you're making an effort to engage the audience with some Mathematics etc.
I wish you well.

I'll hide everything else under a spoiler because it's a bit dull and might prevent others from making their comments.

Spoiler: show

   The main reason for not counting 1 as a prime number is that most of the results we have about prime numbers, or more generally about whole numbers, won't work if you tried to state them as they are now and continued to use the term "prime number" in that statement of the result.   The decision not to include 1 as a prime number wasn't really done because of some elaborate definition or way of identifying what the primes are supposed to be.   I don't think following a pattern that emerges from dots had a lot to do with it.    Instead, it was done because it's not all that useful to have 1 included in the set.

    Another way to say this is that there's no reason you couldn't include 1 as a prime number if you want to.   You go right ahead and do that.   You don't even need to make up a good reason like drawing an arrangement of dots.   For whatever reason, you can put the number 1 into the primes if you like.   The only change that will result is that mathematicians will stop quoting their results by referring to "prime numbers" .  Instead they will identify a slightly different set of numbers, let's call them "Q-rimes" and their results will be stated with respect to that.   The Q-rimes will naturally be your Primes excluding the number 1.  So, the only thing that will have happend is that you will have changed the name we apply to describe what is currently called the prime numbers.

    I suppose to finish this I should give at least one example of a result that is useful and easily stated with reference to prime numbers (with 1 excluded but not if 1 is included).

     The fundamental theorem of arithmetic
Every counting number can be written as a product of prime numbers each raised to an appropriate (Natural number) power.   Furthermore, that respresentation is unique up to changing the order in which you perform the multiplication.

Example:     40  =  2³ x  5
   If you try to write 40 as some other product of primes, let's say you allow yourself to use three prime numbers   p, q, r    such that   40  = p^a x q^b x r^c     for some exponents  a,b,c   then you find that you can't,  there's no solution for that.     The fundamental theorem of arithmetic holds.
    However, if you allowed 1 to be a prime number then you can.....   One solution is to set p = 2,   q = 5, r = 1    and a= 3, b = 1, c= 2 .  That will be another representation of the number 40 as a product of primes:    40  =  2³ x  5  x  1²     and so the fundamental theorem of arithmetic doesn't hold.

Is 2 really a prime number?

    Actually 2 is another number that has very unusual properties even though it is prime.   It is often very useful and desirable for mathematicians to consider a subset of primes that doesn't include 2.   They call this set the "odd primes" and several theorems are stated with reference to  "odd primes" instead of just "the primes".  Alternative terms exist for this set and it's quite common not to bother naming the subset and just write a result as holding  "for all primes, p > 2".
   So 2 is a prime number but its certainly not typical of primes and there is a similar set, the odd primes, where you do just exclude it.

Best Wishes.

6

Physics, Astronomy & Cosmology / Re: Can sand/salt permanently molecules absorb resonate frequency?

« on: 22/02/2022 20:28:31 »

The patterns formed on Chladni plates are a result of the properties of the plates themselves, and has nothing to do with the sand/salt/sugar/dust/etc. placed on top for visualization purposes. ..... The pattern that the nodes make is a function of the frequency of the vibration and the size/shape of the plate.

Fully agree, acid test is that the pattern changes with frequency, so there is no memory effect.
PS I use tea leaves, but don’t read anything into that 

7

General Science / Re: co2 bomber extinguisher

« on: 16/01/2022 16:01:51 »

Hi. I come up with extinguisher that can kill forest fires. I call it CO2 bomb.

Looks like American-football ball, but bigger. inside is lots of liquid CO2.
Drop one in the forest fire. Valves will open and release huge amount of liquid CO2, which will become gas. 

Fires need heat fuel and oxygen, you need to remove one to extinguish the fire. You cannot reliably remove the oxygen from a fire for a sustained period, nor the fuel in any reasonable scenario using fire suppressants etc, so you need to remove the heat. Extinguishing the fire may remove the heat from a small fire long enough to cool the fire but a large fire needs cooling down a great deal, this is why the fire brigade spend long periods dampening fires and raking through material piles.

Co2 from solid to gas I would bet has a far smaller  energy requirement than liquid water to gas.

8

General Science / Re: Is this a feasible system for recycling CO2?

« on: 07/01/2022 16:55:47 »

Alan, don't you work with MRIs? I assume you know what happens when a magnet quenches...

Indeed. But suffocation incidents are usually associated with the loading and cooling process, not a subsequent quench. We have exhaust stacks to vent quench gas safely once the magnet is assembled.
My own MRI units  used room-temperature resistive magnets or high-temperature supercons cooled with gaseous helium, but now I'm working with other people's kit, fraught with the dangers of liquid refrigerants.
Fortunately modern MRIs don't use nitrogen - one less problem - and capture helium boiloff, saving a lot of money. Time was that liquid helium was cheaper than beer when vast quantities were used for North Sea divers maintaining oil and gas rigs, but so much was exhausted to the cosmos that it is now more expensive than champagne.

9

Physics, Astronomy & Cosmology / Re: Energy loss in electrolysis

« on: 11/11/2021 08:41:49 »

If you want light energy...

...Heat a piece of quicklime with your oxyhydrogen torch.

10

Technology / Re: What are some low-tech ways to address climate change?

« on: 08/11/2021 07:34:39 »

A great way to reduce co2 or methane if you believe both to be the cause is to shoot animals, people will even pay you for the privilege.

We fish and shoot already.
Animals aren’t a problem because they release only “neutral” carbon into the atmosphere. They release large amounts of CO2 and methane but their carbon source is limited to plants or animals that eat plants and plants get their carbon from the atmosphere. So, their only source of carbon is indirectly from the atmosphere and they only cycle carbon back to the atmosphere from whence it came. They do not cause a net gain in the amount of carbon. They recycle what is already there.

If it were not for animals, decomposition, insects, and fire would continue to recycle CO2 and methane back into the atmosphere in their place. If animals ate non-neutral carbon sources like coal or oil, that would be a problem because they would be releasing carbon from 300 million years ago back into the atmosphere and contribute to the net amount of atmospheric carbon. Fossil fuels are the problem. 

11

General Science / Re: What's 0^0 ?

« on: 03/11/2021 00:53:20 »

Hi.

You're doing well there @hamdani yusuf .
   You've already got enough to see that real numbers raised to some exponenet aren't always equal to a real number.

Sometimes, you can't find any real number that would be suitable.   Sometimes you can find many suitable Real numbers.  It's quite natural to extend the scope of the problem to consider complex numbers but then you can sometimes find an infinite set of numbers as a solution.

You already have enough evidence to recognise that 0⁰  was never required to be a unique Real number.  It's not even required to be a unique Complex number.  You've also presented enough examples to see that it cannot be defined as a real number in any consistent way.   If it has to be anything, it could be a bicycle.  It's just a collection of mathematical symbols we can write down but it's not representative of any numerical value.   ∀6†12  is another set of symbols that doesn't equal or represent any numerical value.

   Technically,  x^1/n  is defined to be the positive root wherever there was a choice.  So that  9^1/2 is +3 and nothing else.   This is done because it maintains exponentiation as a well defined function for as long as possible.   Anyway, using that it would mean that your answer to q. 4 is wrong.
   If you were given the expression    (x²)^1/2  = x      and then set x= -3    then you would have to deduce that  +3 = -3.   
   Obviously we don't really want anything that silly, so the only possibile resolutions are that we give up on considering a^b  as a well defined function for all a,b ∈ Z   OR ELSE   accept that the given equation   (x²)^1/2  = x  was not valid for all x∈ℜ.
   Mathematics has taken the second option,   the rules of manipulating indicies that we were taught in school do not hold for all real numbers as a base for the exponentiation.  A good teacher might have brought that to the attention of their students but it wouldn't matter much anyway:  As human beings we want to follow patterns and we want to extend these patterns wherever we can, so we would have ignored any warning.
   Thus (x^m)^1/n  = x^m/n  is only a true statement for some values of x.  The original question 4 that I presented was a little misleading.   The most appropriate response should be "Exponentiation cannot follow this rule even though it seems like it should (because otherwise +3 = -3)". 
    I needed this to be considered because there are so many misconceptions and false proofs based on using "rules of indicies" even though these rules do not and cannot hold in the system of mathematics we commonly use.

Best Wishes.

12

General Science / Re: What's 0^0 ?

« on: 02/11/2021 17:49:40 »

Hi.

   The original question was:

What's 0 to the power of 0?

    This is actually a very good question and it's something that isn't easily resolved. 
    It also turns out that whenever something like 0⁰ is encountered in science, it has nearly always arisen as a Limt of x^x  as  x→0+    (approaching 0 from the right).   This limit is defined and does equal 1.   As a consequence of this it has become an un-official convention that  0⁰ = 1   and  regrettably many calculators, like the one you were using, will show you that result.

   Too often we start from a false assumption.  It is easy to imagine that just because we can write some mathematical term down it must have some numerical value.  For example, I have never calculated the value of 10067 + 765409 but I might assume it is some Real number.  We also frequently assume that when there are patterns to follow we must be able to extend those patterns.  For example, whatever my answer to that sum might be it should be bigger than the first number, 10067.
  For exponentiation it's actually much safer if we start by assuming nothing at all.  Do not assume a^b defines any function from (a,b) → ℜ   and  don't even assume that the Real numbers exist.  Instead start from more basic assumptions (axioms).   If we do build up the Real Numbers and develop enough real Analysis to construct the exponential series then we will see that 0⁰ was never defined and indeed it cannot be defined in any consistent way as a Real number.

    I could just spit out some chapters from a textbook on Real Analysis or Complex Analysis that talk about the exponential series but I can't do that any better than the textbooks.  Instead let's put out some minor problems to consider, which might help to identify just how complicated it is to raise numbers to an exponent:

   1.    What  is   4^1/2 ?     Why?
   2.    What is    (-4)^1/2 ?   Is there no real solution?
   4.    By the rules of indicies we have (x²)^1/2  = x   for all x.  This seems reasonable but what happens to the LHS and  RHS  when you let x = -3 ?    Don't we obtain  +3 = -3  ?
   5.    3^π  cannot be written as the  integer root of any integer power.  Specifically  3^π ≠ (^a√3)^b  for any inetgers a,b.   So what is the value of  3^π?   Could it be a negative number?    If that's too easy  consider   (-3)^π .

Best Wishes.

PS,  yes I know question 3 was missing.

13

That CAN'T be true! / Re: Why can't water vapour be the driver of today's climate change?

« on: 02/11/2021 11:54:08 »

Even if CO2 were a plausible driver of historic temperature, we still need to find a reason why its concentration varied in the way it did.

Historical causes of warming are beside the point, what humans are doing is a unique situation.

14

General Science / Re: What's 0^0 ?

« on: 02/11/2021 09:44:22 »

y = x^x is well-defined for all x < 0.

What does it mean? Doesn't it mean all negative x?

15

That CAN'T be true! / Re: Why can't water vapour be the driver of today's climate change?

« on: 02/11/2021 08:45:49 »

"Why can't water vapor be the driver of today's climate change?"
Because it falls out of the sky when there's too much of it.
This is not news to anyone in the UK.
It did it a thousand years ago, and it still does it today.
So the  amount of water in the air is essentially fixed .

It can, of course, be "driven", but it can't be the driver.

16

That CAN'T be true! / Re: Why can't water vapour be the driver of today's climate change?

« on: 29/10/2021 13:29:59 »

"

Evidence is one thing,

And what you presented is another; at least  in regard to what you said.
You actually said  this

water is indeed the problem, and as the ice core data shows, always has been.

The ice core record (ironically) does not tell you about water levels in the air.

If you really think it does then please give us a link.

I cannot find a rational interpretation consistent with CO2 being the driver of historic climate change.

Good point- sort of.
But inevitable and meaningless.

It is true that the historical record does not show CO2 leading a temperature rise.
But that's because, prior to mankind getting in on the act, there was no plausible source of CO2 that could materially affect the concentration in the atmosphere.

You will not see, at any point in Earth's history a record of what happened when mankind suddenly raised CO2 levels roughly 10 times faster than they have every risen before.
Because mankind never did it before.

That's more or less the point of anthropogenic climate change. Nobody ever did it before.
So it makes no real sense to look at the historical record for a precedent for "today's" events - say the last 200 years.
Historical climate change was not driven by anthropogenic CO2.

Nobody said it was.


But here's the actual explanation of the link between CO2 and climate.
TLDR version, it's not been the cause in the past; it has been an amplifier- a positive feedback mechanism  enhancing changes due to orbital effects.

But it still has the effect of creating warming, even if the initial source isn't orbital variation, but mankind.

17

Just Chat! / Re: Equal or equivalent?

« on: 21/10/2021 19:07:23 »

In the interests of further confusion, chemists think " equivalent is a unit of quantity.
It's perfectly reasonable to ask you to weigh out an equivalent of zinc.

18

The Environment / Re: What's going on with the climate?

« on: 20/10/2021 17:12:22 »

Aren't there ways to just suck up the  CO2 back from the environment?

Plant trees - or just stop cutting them down.

19

Physics, Astronomy & Cosmology / Re: Can we ever truly describe space as empty?

« on: 20/10/2021 13:15:31 »

Are fields objects? Are they objects with the potentiality to become "things"?

'Object' connotes a 'thing' which has a property of location, velocity, exists for a duration within time, etc.
A field has none of these things and is thus not an object by any reasonable definition.
For that matter, 'universe' fails to meet any of that criteria and much confusion results from treating it as one.

Take the field 'altitude' for instance. The surface of Earth has, everywhere, an altitude, and thus the field can be measured anywhere. It doesn't have a location since it is defined for all points on the surface. It has no potential to become a thing, but since Earth anchors it, it would (unlike something like the EM field) cease to be meaningful if Earth ceased to exist.

20

General Science / Re: What preposition does one use for a mirror image?

« on: 19/10/2021 08:33:13 »

Via the mirror