How does drift velocity vary with temperature? Does it increase or decrease?
122211
How does the drift velocity of electrons in a conductor depend on the temperature?  I have two contradicting views for this.    First, we can say that increasing the temperature of the conductor will increase the kinetic energy of the electrons. Hence, their drift velocity should increase with increase in temperature.  Or, from the relation $v_d = \frac{eE}{m}T$ ($T$ is the relaxation time) we can say that the drift velocity is directly proportional to the relaxation time. Increasing the temperature will obviously decrease the relaxation time - as collisions will become more frequent - and thus decrease the drift velocity. Hence, an increase in the temperature will cause a decrease in the drift velocity.   So which view is correct?
26988
Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite value. A change is velocity is acceleration, so the value of the acceleration would have to increase from zero to some value. You would also need to increase the jerk from zero to some value to have a change in acceleration.  Is there an infinite series of higher derivatives of position for this to work? Or am I missing something?
46021
Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens with $\Delta x$ as we go forward in time? Does it have to increase at all times? Or is there a counter-example where the uncertainty in position is decreasing, if even for a short time period?  My initial guess is $\Delta x$ must always increase, because $p \neq 0$, so that $\Delta p \neq0$ and hence $\Delta v = \frac{\Delta p}{m} \neq 0$. But if there's a spread in velocities, then the wave packet must also spread. Is this logic correct? Or could we have a wave packet where the back of it would move forward faster than the front, and for a certain period until that back end catches up with the front one, it would actually be narrower than at the outset, i.e. reducing $\Delta x$? If yes, how would one describe such a free particle (wave packet)?  So it does seem to me that every wave packet describing a free particle will eventually spread, but the question is whether there can be a time period in its evolution when it is actually becoming narrower.  edit: In particular, if it does not have to increase at all times, can this be shown without appealing to time reversal?
61903
Combining the first and second law of thermodynamics we can get the following equation  $$TdS=dU-P_{ext}dV$$  First question: Is this equation applicable for irreversible processes such that that $dS≠\dfrac{dQ}{T}$?  Second question:If the system temperature $T_{sys}$ is smaller than the surrounding temperature $T_{sur}$, which temperature should we put in the equation?   I have this question because sometimes people use $T_{sur}$ instead of $T_{sys}$ (e.g. , ) but the equation is supposed to describe changes in the system.
962
I am confused whether drift velocity depends upon area or not . I checked answers for this question but all of them were cancelling each other out . from the equation $$I = neAv$$ It is clear that drift velocity should depend upon area but at the same time don't you think that by increasing the area of cross section of a conductor should have resulted in increase in drift velocity please help me out with it in detailed answer of how should i go with all the possible cases and explanation ,thanks :)
116781
So I know that if you increase the voltage across a wire then the current will increase. But an increase in current leads to a increase in heat production though $P=I^2R$, but as the temperature increase the vibrations of the metal ions increase and so the current is more restricted implying the resistance increases. But as the resistance has increased, the heating has increased again and this will go in a cycle leading to infinite resistance and heat production so where am I going wrong?
55195
I was reading a textbook. I found that it was mentioned the speed of sound increases with increase in temperature. But sound is a mechanical wave, and it travels faster when molecules are closer.   But an increase in temperature will draw molecules away from each other, and then accordingly the speed of sound should be slower. How is it possible that the speed of sound increases if temperature increases? What is the relation of speed of sound and temperature?
38503
I saw  Nature article today, which cites e.g. . And it makes no sense to me. The temperature of a collection of particles is the average kinetic energy of those particles.  Kinetic energy cannot be less than zero (as far as I'm aware), so I don't understand what this article is trying to say, unless they're playing around with the conventional definition of &quot;temperature&quot;. The only thing I can think of is if you have something like this: $$\frac{1}{kT} ~=~ \left(\frac{\partial S}{\partial E}\right)_{N,V}$$ And they've created a situation where entropy decreases with increasing energy.
70429
In the derivation of drift velocity I have seen two variations and want to know which one's correct.   $s=ut+\frac{at^2}{2}$ Assume that the drift velocity of any electron in any conductor is : $$\vec{v_d}=\frac{\vec{l}}{t}$$ Due to the electric field the acceleration of electrons in any conductor is: $$a=\frac{-e\vec{E}}{m}$$ Now the distance travelled by an electron after a long time (initial thermal velocity = 0) $$l=\frac{at^2}{2}\implies \frac{-e\vec{E}t^2}{2m}$$ the time between the collisions is $\tau$ $\therefore$ $$l=\frac{-e\vec{E}\tau^2}{2m}$$ thus the velocity is $$\vec{v_d}=\frac{-e\vec{E}\tau}{2m}$$ In another proof I saw the author using $v=u+at \implies v_d=\frac{-e\vec{E}\tau}{m}$   My question is which of the the two equations of motion can be used in the proof? Can they be used at all.
56448
There is this puzzling thing that is called : paradoxically, warm (35°C) water freezes faster than cold (5°C) water.  As a physisist, I've been asked about it several times already. And I have no definite answer to that, apart from the standard: "there are many things that can influence it".  So, does anyone knows about the status or progress on that effect? Any recent reviews, publications or other references?
11832
I suspect this has something to do with thermodynamics and the  and I'm interested in a mathematical derivation of this result.
88405
Has anyone understood the ? What is the current status?  In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's engine) How does one account for thermodynamic concepts applicable to situations involving measurement? What does it mean to reset the state of the apparatus why is free energy expended in the process?
15965
In my textbook, a relationship is plotted between the resistance of the material and the temperature, and the temperature coefficient is defined as the slope of that graph divided by an arbitrary resistance $R_1$ on the graph. Does that mean that the coefficient varies depending on the temperature I choose to divide the slope by?  If so, how does it stand as a valid reference to the material’s resistance growth rate with temperature?  If not, then where did I go wrong with this train of thought?
101030
According to thermodynamics every adiabatic system and (with no external energy added) will reach thermodynamic equilibrium or an ergodic state (2 law of thermodynamics entropy can not decrease in a closed system). State at which Temperature (or mean kinetic energy of the particles) will be same everywhere. So the answer to the question should be simple and straightforward $dT/dh = 0$. But is it the case? Let's open  page on Wikipedia and will see that adiabatic system will always create and support gradient $$dT/dh &lt; 0$ and equal to some constant. One can argue that this is because this system do not reach equilibrium and do not relax much. But look at calculation, if some additional relaxation took place then the gradient must decay and reach 0 at some time, but it is not the case. One can argue and say that ok gradient is there but there is no contradiction with second law. But a thought experiment conducted by Maxwell with two columns of different gases. He showed that if the calculations are correct, then gradients of different magnitude will be generated in these columns. And therefore, in a system where these two gas columns are isolated everywhere except at the top, there will certainly be a flow of heat from a colder body to a hotter one. Also, because gradient is exists Boltzmann distribution are mistaken. It is simply striking how two such contradictory statements, namely the universality of the second law of thermodynamics and the gradient in the gas column in the gravitational field, are able to coexist, this is pure schizophrenia. I also made a simple computational model which clearly shows that adibatic lapse rate you can find it on  or in the answer of this question. Here I list some findings which I made while discussed this question and made my model:  If you consider collisions of perfect gas particles it always leads to just velocity exchange (Newton's cradle as analogy), this statement can be easily proved mathematically, because masses are the same and collision are rigid and radius of the particle is negligible. This is the real reason why you should not take into account perfect gas collisions because it does not introduce into the model any new properties.  Despite the fact that Boltzmann and others derived their distributions for an ideal gas, implying the property of ergodicity of the system, in reality there is no energy mixing for the ideal gas model and particle collisions will not help at all here (see the previous paragraph). In reality, a certain entity is needed that would mix the energies of the particles and I introduced such an entity, and just after that the gradient manifested itself in all its glory.
4669
If voltage is a potential difference, describing how much energy will be lost per unit charge as charge carriers pass through the resistor, why would the rate at which charge flows (i.e. current, $=dq/dt$) affect the amount of energy lost per unit charge?  I suppose I am asking why a quasi-"extensive" property of the system (current) would affect a quasi-"intensive" property of the system (voltage drop across the resistor).  Apologies if the answer is obvious; I was having trouble understanding why the rate of charge flow would factor into voltage drop whilst trying to rationalize Ohm's law for myself.
31480
This is a strange question I would like to have some explanation accompanied with:  We have an ice block, with in it a lead block. This entire block is put into a glass of water, resulting in a rise of water level until the edge of the glass. The block stays floating on the surface. What will happen with the water level when the ice melts?  The answer is that it will drop, but how is this even true?? My thoughts are: - block floats on water, so rho(block) &lt; rho(water) - Archimedes law, the Fg of block = Fg of water pushed away. - Since a smaller volume of water has equal mass (and so Fg) to block, and ice is less dense than water, when it melts, no mass is lost, so it will take in less space??? Please help me with this point of thinking.
47210
A  posted on Youtube.  How does this phenomenon work? I know he is using frequency to propagate water in a sine/cosine wave, but how does it exactly work this way? Why do we see it as if its paused, or in slow motion, or even in reverse?  Can someone please explain this? I am intrigued by the video and want to know it's physics.