http://www.physicsforums.com A community for scientists to discuss physics topics. Physics help is offered to students, along with career and academic counseling en Sun, 19 May 2013 11:18:51 GMT vBulletin 60 http://www.physicsforums.com/images/physicsforums/misc/rss.jpg http://www.physicsforums.com http://www.physicsforums.com/showthread.php?t=692478&goto=newpost Sun, 19 May 2013 09:29:43 GMT Hello everybody, I registered here hoping to finally find a fundated answer about what I by myself seem not be able to figure out. Question in... Hello everybody,

I registered here hoping to finally find a fundated answer about what I by myself seem not be able to figure out.

Question in short:
We have calculated a list of wavenumbers for some molecular systems. How do you get the vibrational partition function from that?

My problem in detail:
Let's take this list of wave numbers as an example:

[cm^-1]
1602,13
3710,78
3829,60
(this is for one water molecule)

Now my collegue explained to me that it's correct to calculate the vibrational partition function as
[itex]q_{vib} = \frac{e^{{-h \nu}/{2kT}}}{1-e^{{-h \nu}/{kT}}}[/itex]
for each frequency and then multiply them all.
Which would give

[itex]q_{vib,1} = 0,020806[/itex]
[itex]q_{vib,2} = 0,000127[/itex]
[itex]q_{vib,3} = 0,000096[/itex]
[itex]q_{vib,tot} = 2,53E-10[/itex]

which seems really weird to me because the partition function becomes lower and lower with every vibrational mode. Can a partition function even be lower than 1?

One of the few things I could find about this is this one, page 5, eq. 3.21 to 3.22: http://www.chem.iitb.ac.in/~bltembe/pdfs/ch_3.pdf
But isn't the zero of energy scale kind of arbitrary?
Anyway, using
[itex]q_{vib} = \frac{1}{1-e^{{-h \nu}/{kT}}}[/itex]
gives

[itex]q_{vib,1} = 1,000433438[/itex]
[itex]q_{vib,2} = 1,000000016[/itex]
[itex]q_{vib,3} = 1,000000009[/itex]
[itex]q_{vib,tot} = 1,000433463[/itex]

which seems way more reasonable to me. (Right? :blushing:)

But it leaves open the question of the zero of energy scale for me. My collegue insists that it's arbitrary where you put it, so both solutions should be correct. But since it gives a factor into each of the single partition functions, how can it be equivalent? Also, would [itex]{h \nu}/{2kT}[/itex] be the correct zero?
Is it even correct to just plainly multiply the single vibrational partition functions?

Thanks for any help. Sorry for the long question, I'm just really confused about this.
Ciao!

Giogio ]]> Atomic, Solid State, Comp. Physics Giogio http://www.physicsforums.com/showthread.php?t=692478 http://www.physicsforums.com/showthread.php?t=692474&goto=newpost Sun, 19 May 2013 09:09:32 GMT My question is: since there exists a Plank time and a Plank distance, is it true or false that any speed and the speed of light in particular must... My question is:
since there exists a Plank time and a Plank distance, is it true or false that any speed and the speed of light in particular must be a multiple of (Plank distance)/(Plank time) ?

Am I saying something nonsense ? ]]> Quinzio http://www.physicsforums.com/showthread.php?t=692474 http://www.physicsforums.com/showthread.php?t=692469&goto=newpost Sun, 19 May 2013 08:23:22 GMT Say, a body of mass 'm' is thrown at a certain angle with the vertical with certain initial velocity 'u'.
The initial momentum of this object is mu.
Am I right to say that if it spent 't' seconds in flight and came back, its final velocity will still be 'u'?
And the change in momentum will be mu-(-mu)=2mu?
And would this be correct or not:
F=dp/dt
=>dp=F*dt
Since F=mg and dt=t, change in momentum=mgt?
One of these has to be wrong. I don't know which one. ]]> Classical Physics s0ft http://www.physicsforums.com/showthread.php?t=692469 http://www.physicsforums.com/showthread.php?t=692467&goto=newpost Sun, 19 May 2013 08:02:30 GMT what is the mechanism by which light changes its speed and wavelength while travelling from one medium to other. I know it is c/n or lamda/n and know... what is the mechanism by which light changes its speed and wavelength while travelling from one medium to other. I know it is c/n or lamda/n and know it comes from maxwells equations, but what is the physical reason behind this? ]]> Classical Physics shantanuphadke http://www.physicsforums.com/showthread.php?t=692467 http://www.physicsforums.com/showthread.php?t=692464&goto=newpost Sun, 19 May 2013 06:54:09 GMT Why can't quantum behavior be explained as an extreme version of classical behavior?

For instance, the idea of a small quantum particle being in superposition could be explained by that particle switching between 2 or more states at an extremely high frequency. How high a frequency? Well, on the order of a Planck Length or Planck Unit.

The only addendum to classical behavior that would be required would be non-locality or tunneling (ie. macroscopic objects are too big to tunnel, but quantum-sized objects are small enough to squeeze through the cracks) ]]> Quantum Physics sanman http://www.physicsforums.com/showthread.php?t=692464 http://www.physicsforums.com/showthread.php?t=692454&goto=newpost Sun, 19 May 2013 05:13:55 GMT I'm reading Classical Mechanics (Taylor), and the 6th chapter is a basic introduction to calculus of variations. I'm super confused :confused:

I've tried to go to other sources for an explanation, but they just make it even worse!

So, let me see if I can get some help here.

[tex]\int^{x_{2}}_{x_{1}} f(y(x), y'(x), x)dx[/tex] - the integration of a function of three variables. y(x) is an as yet unknown curve. I understand that although f(y, y', x) is a function of three variables, it is only dependent on one variable, x. (where do these come from, exactly?)

Taylor then defines Y(x) = y(x) + η(x) is the WRONG path, where y(x) is the correct one. η is the variation of Y(x) from y(x). - why do we need to introduce the INCORRECT path?

Next, he introduces α into Y(x) = y(x) + αη(x). If we set α = 0, we will have Y(x) = y(x) - why do we need α?

Our integral now becomes: [tex]\int^{x_{2}}_{x_{1}} f(y(x) + αη(x), y'(x) + αη'(x), x)dx[/tex] - we're assuming that α is equal to 0? I'm not sure I 100% understand this step.

We need to check that [itex]\frac{dS}{d\alpha} = 0[/itex]- is this to check that α is a constant? or used as a way of making sure α = 0?

Take partial derivative: [tex]\frac{\partial f ((y(x) + αη(x), y'(x) + αη '(x), x)}{\partial \alpha}= \eta \frac{\partial f}{\partial \alpha}+ \eta ' \frac{\partial f}{\partial y'} [/tex] - because of the chain rule


[tex]\frac{dS}{dα}=\int^{x_{2}}_{x_{1}}\frac{\partial f}{\partial α}dx = 0[/tex] -

Next he works some voodoo magic by using integration by parts on the integral. I haven't worked this step out myself, but I assume it's straight forward.

So, in the end, we get: [tex]\frac{\partial f}{\partial y}-\frac{d}{dx}\frac{\partial f}{\partial y'}= 0[/tex]

So, I'm pretty lost. I think it would help if I understood the idea of what we're really doing here. This is essential arc length along the shortest curve, but all the additional variables and what not are confusing the hell out of me.

Sorry for the long post, but any help is much appreciated. I'm so desperate, I'm offering a reward of one (1) virtual cookie to the first helpful post.

NB - I put this in the Classical Physics section, because I'm more concerned with how this is used in mechanics right now. Although I'm interested, in what course is Calculus of Variation taught in at a rigorous level? ]]> Classical Physics Astrum http://www.physicsforums.com/showthread.php?t=692454 http://www.physicsforums.com/showthread.php?t=692452&goto=newpost Sun, 19 May 2013 05:09:33 GMT Frictional Force is mathematically defined as:

Ff = μ*m*g*cos(θ)

, where μ is the coefficient of friction, m is the mass of the object, g is the acceleration due to gravity and θ is the angle of the inclined plane.

But in terms of direction, this makes no sense!

Suppose there is an object on an inclined plane. It is going to travel down the plane because its Weight Force is pulling it towards the Earth. At the same time, a Frictional Force will act in the opposite direction to the motion of the object.

The Frictional Force, however, is calculated using the object's Normal Force times cos(θ) (times μ), which acts perpendicular to the surface of the plane. But this means that the Normal Force is not acting in the same axis as the Frictional Force, so how can Normal Force times cos(θ) (times μ) be used to calculate Frictional Force?

Let me elaborate: In order to calculate Normal Force in the same axis as Frictional Force, you should use μ*m*g*sin(θ), not μ*m*g*cos(θ). Would it not make more sense this way?

I'm either very frustrated or very confused. Maybe a diagram with your answer can help.

Thank you. ]]> Classical Physics FredericChopin http://www.physicsforums.com/showthread.php?t=692452 http://www.physicsforums.com/showthread.php?t=692451&goto=newpost Sun, 19 May 2013 04:26:56 GMT 5 years ago I was at penn state, for engineering of all things. I did things similar to this but everything is eluding me at the moment. My... 5 years ago I was at penn state, for engineering of all things. I did things similar to this but everything is eluding me at the moment.

My situation:

I have a car that Ive attached a class 1 trailer hitch. Its rated at 2000lbs and i don't intend on towing more than 1000 lbs.

For a peace of mind, id like to have an extra safety barier.

Id like to run some steel cable from the hitch itself to the frame of the car (the hitch is bolted to the frame).

The cable should prevent the trailer from taking off in an even the trailer hitch fails.

Consider the maximum speed of 75.

I know deceleration/acceleration is important here, numbers im not sure if I can reliably provide. ]]> General Physics The450Man http://www.physicsforums.com/showthread.php?t=692451 http://www.physicsforums.com/showthread.php?t=692448&goto=newpost Sun, 19 May 2013 03:48:00 GMT Hi, I have a question regarding reciprocal space symmetry operations and would appreciate if somebody can answer that: Lets say I have two k... Hi,

I have a question regarding reciprocal space symmetry operations and would appreciate if somebody can answer that:

Lets say I have two k points, k1 and k2, in reciprocal space which are symmetric to each other. Since these two kpoints are symmetric to each other phonon scalar properties like frequency, lifetime, etc will be same for k1 and k2. Similarly, vectors like group velocity have same magnitude for k1 and k2. I am wondering how are vector components related at k1 and k2?

Thanks a lot in advace! ]]> Atomic, Solid State, Comp. Physics pinkuagarwal http://www.physicsforums.com/showthread.php?t=692448 http://www.physicsforums.com/showthread.php?t=692442&goto=newpost Sun, 19 May 2013 02:53:55 GMT In β+ decay a proton releases a positron and an electron neutrino causing the proton to change into a neutron to help balance the nucleus. I am studying advanced PET imaging and trying find a better understanding of the positrons other half. Does it just go on being a normal electron. ]]> High Energy, Nuclear, Particle Physics cameljoe11c http://www.physicsforums.com/showthread.php?t=692442 http://www.physicsforums.com/showthread.php?t=692437&goto=newpost Sun, 19 May 2013 01:35:01 GMT I'm reading through the book Quantum Mechanics (Second Edition) by David J. Griffiths and it got to the part about proving that if you normalise a wave function, it stays normalised (Page 13).

That part that I don't get is how they say:

## \dfrac{i \hbar}{2m} \left( \Psi^* \dfrac{\partial^2 \Psi}{\partial x^2} - \dfrac{\partial^2 \Psi^*}{\partial x^2} \Psi \right) = \dfrac{\partial}{\partial x} \left[\dfrac{i \hbar}{2m} \left( \Psi^* \dfrac{\partial \Psi}{\partial x} - \dfrac{\partial \Psi^*}{\partial x} \Psi \right) \right] ##

How can they just pull out a partial operator like that?
Because if you expand it out again it would give you:

## \dfrac{i \hbar}{2m} \left( \dfrac{\partial}{\partial x} \left[ \Psi^* \dfrac{\partial \Psi}{\partial x}\right] - \dfrac{\partial}{\partial x} \left[ \dfrac{\partial \Psi^*}{\partial x} \Psi \right] \right) ##

The operator will be applied to the wrong ## \Psi ## and also won't you need to apply the product rule to is as well? ]]> Quantum Physics Cogswell http://www.physicsforums.com/showthread.php?t=692437 http://www.physicsforums.com/showthread.php?t=692433&goto=newpost Sun, 19 May 2013 01:27:35 GMT I just found out that if you're exposed to the vacuum of space, you won't explode, but rather you'll die less excitingly from a lack of oxygen. So much for the scientific accuracy of total recall!

How is that a vacuum doesn't "pull" matter apart given that lowering pressure can decrease boiling/melting points? Doesn't a really low pressure equate to really low boiling points? Is it because the vacuum in space isn't perfect? ]]> General Physics mrquantum http://www.physicsforums.com/showthread.php?t=692433 http://www.physicsforums.com/showthread.php?t=692423&goto=newpost Sun, 19 May 2013 00:01:12 GMT I am trying to calculate the volume of liquid water i need to place in a sealed container in order to obtain 10 psi of steam pressure in that closed... I am trying to calculate the volume of liquid water i need to place in a sealed container in order to obtain 10 psi of steam pressure in that closed container.

Here are the numbers:

Temp: 816 C
Volume of steel pipe: 154.497 ml
Final pressure: 10 psi

If I left out a required number please let me know.

If you could show how you solved it or what equation you're using that' be great.

Thanks in advance to whoever helps me out! ]]> Classical Physics jackal67347 http://www.physicsforums.com/showthread.php?t=692423 http://www.physicsforums.com/showthread.php?t=692422&goto=newpost Sat, 18 May 2013 23:57:45 GMT Is there any way to create an isolated point charge without any contact with the matter which one wishes to charge? I recognize that this would mean... Is there any way to create an isolated point charge without any contact with the matter which one wishes to charge? I recognize that this would mean stripping off electrons from the substance, so I suppose my question is: is there any way to strip off electrons without having to specifically contact the object which one wishes to charge? ]]> General Physics res3210 http://www.physicsforums.com/showthread.php?t=692422 http://www.physicsforums.com/showthread.php?t=692411&goto=newpost Sat, 18 May 2013 22:04:13 GMT Hello, I want to do an experiment in hydrogen gas H2 (1 bar) and I want to simulate the maximum amount of H+. What is the best way to get the largest... Hello, I want to do an experiment in hydrogen gas H2 (1 bar) and I want to simulate the maximum amount of H+. What is the best way to get the largest fraction of H+ with minimal energy input? Thanks. ]]> Atomic, Solid State, Comp. Physics edpell http://www.physicsforums.com/showthread.php?t=692411