Tagged Questions
5
votes
4answers
180 views
Can a single molecule have a temperature?
A show on the weather channel said that as a water molecule ascends in the atmosphere it cools. Does it make sense to talk about the temperature of a single molecule?
2
votes
3answers
139 views
What is the general statistical definition of temperature?
Temperature in an isolated system is defined as:
$$\frac{1}{T} = -\frac{\partial{S(E,V,N)}}{\partial{E}} $$
But I wonder how one can generalize this to a random system.
Or for instance to a point in ...
2
votes
2answers
131 views
Why is the temperature zero in the ground state?
This is probably a simple question: I see this claims in many books, but I can't figure a reason why this is true.
So my question is why this claim is true:
"If we know that the system is in the ...
2
votes
2answers
58 views
What is the derivation for the exponential energy relation and where does it apply?
Very often when people state a relaxation time $\tau_\text{kin-kin}, \tau_\text{rot-kin}$,, etc. they think of a context where the energy relaxation goes as $\propto\text e^{-t/\tau}$. Related is an ...
2
votes
1answer
44 views
Temperature of a small system
What is wrong if I define temperature of a small system (I mean, a system which has not a large number of particles) by
$$1/T = dS/dE$$
?
1
vote
1answer
152 views
Absolute zero and Heisenberg uncertainty principle
I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and ...
2
votes
2answers
148 views
Why the temperature is getting lower when the universe is expanding
As we know, if an ideal gas expands in vacuum, as its energy is unchanged, the temperature remains the same. An ideal gas's energy does not depend on volume. In general, the energy is $kT$ times the ...
3
votes
2answers
114 views
Any example of lower symmetry in high temperature phase than the low temperature phase?
All the phase transition cases I came across so far have this property: the lower temperature phase has lower symmetry than the higher temperature one. But it is nowhere explicitly said that, lower ...
8
votes
3answers
270 views
Could temperature have been defined as $-\partial S/\partial U$?
When coming up with a definition of temperature, it's typical to start with an empirical definition that a system with a hotter temperature tends to lose heat to a system with a colder temperature. ...
0
votes
1answer
232 views
How much energy Maxwell's demon will earn?
Suppose we have one mole of one-atom ideal gas at temperature $T$.
Suppose Maxwell's daemon has separated molecules into two sections, one with speed below mean and another with speed above mean.
...
5
votes
2answers
333 views
The analogy between temperature and imaginary time
There are many statements about the relation between time and temperature in statistical physics and quantum field theory, the basic idea is to interpret (inverse) temperature in statistics as "time" ...
3
votes
1answer
216 views
Limit of Fermi-Dirac distribution as $T$ goes to zero
Hopefully this is a simple question, I just can't seem to get my mind around it.
I'm to take the limit of the Fermi-Dirac distribution for $T \rightarrow 0$.
In this limit the chemical potential is ...
4
votes
4answers
218 views
Why can $\beta$ not be linearly proportional to $T$, that is $\beta = constant \times T$?
$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
4
votes
1answer
136 views
Ideal gas and diatomic gas with same temperature
If a box of ideal gas and another box of diatomic gas are in thermal equilibrium,
does it mean that the average translational energy of ideal gas particle (A) is the same as that of diatomic gas ...
4
votes
3answers
449 views
Is temperature an extensive property, like density?
I was thinking about it some time ago, and now that I've discovered this site I would like to ask it here because I couldn't work it out then.
I know that the higher temperature the air in my room ...
5
votes
7answers
833 views
Is it theoretically possible to reach 0 kelvin?
I'm having a discussion with someone.
I said that it is -even theoretically- impossible to reach 0K, because that would imply that all molecules in the substance would stand perfectly still.
He said ...
11
votes
3answers
880 views
Prove that negative absolute temperatures are actually hotter than positive absolute temperatures
Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
2
votes
4answers
626 views
What does third law of thermodynamics tell us?
I just have a question concerning the third law of thermodynamics.
The third law describes that the entropy should be a well defined constant if the system reaches the ground state which depends ...
4
votes
1answer
270 views
What are conditions for the existence of a critical value (for a phase transition)?
Can there only be a critical temperature if there is some natural unit for an observable in the model, i.e. if there is a natural scale for something? Otherwise I don't see how for a system there ...
2
votes
3answers
191 views
How to “read” the temperature of an abstract system?
How can I interpret the parameter temperature $T$, if I'm not given the description of the system in terms of the equation of state, $E(S,V\ )$ or $S(E,V\ )$ and so on.
In many systems it makes sense ...
4
votes
3answers
686 views
How to understand temperatures of different degrees of freedom?
So I'm reading this book, where after the preface and before the models there is a section called General Notions and Essential Quantities, which introduce some things I don't understand. They regard ...
3
votes
5answers
381 views
Temperature of a System of molecules
Suppose I have a closed system with N molecules in it which are vibrating and all motion equations (rotation, translation and vibration) of the system are known along with any EM field equations in ...
4
votes
5answers
1k views
Is temperature in vacuum zero?
From Wikipedia entry on Kinetic Theory
The temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms.
Now if I remove all the particles from the box shown ...
