c*******n
发帖数: 1648 | 1 Actually I am confused about the definition of temperatrue. I feel like I
didn't learn thermodynamics in college at all. Physical chemists may think
it's
stupid. begging for your answer!
We know that temperature is the average kinetic energy of the system. Say I
have a polymer (or say any liquid) at a constant temperature, and I apply very
high pressure to compress this liquid. Thermodynamically speak, there is no
change of the kinetic energy, which means that vibrational, rotational, and
transl | c*****e
发帖数: 238 | 2
A more accurate relation (which seems to me) is that temperature is a purely
thermodynamically defined thing, namely from the Carnot cycle, and the average
kinetic energy of the system is related to the temperature in classical
statistical mechanics through the equipartition principle, but this is only
valid for gas, not valid for liquid or solid.
For gases, the increase in pressure is purely due to the increase of the
frequency of collisions of gas molecules with the container, their momenta i
【在 c*******n 的大作中提到】
: Actually I am confused about the definition of temperatrue. I feel like I
: didn't learn thermodynamics in college at all. Physical chemists may think
: it's
: stupid. begging for your answer!
: We know that temperature is the average kinetic energy of the system. Say I
: have a polymer (or say any liquid) at a constant temperature, and I apply very
: high pressure to compress this liquid. Thermodynamically speak, there is no
: change of the kinetic energy, which means that vibrational, rotational, and
: transl
| c*******n
发帖数: 1648 | 3 You got very good points, Thank you very much. I missed the conceptual
difference between diffusion coeff. and translational energy for the first
question.
Actually, equipartition principle is still widely used in the most common
molecular dynamics software (like insight) to extract temperatures out from
pure momenta, no matter what substance is, asfar as I know. It seems that
you mean the temperature can not be regarded as the single function of the
kinetic energy for liquids, which means the a
【在 c*****e 的大作中提到】
:
: A more accurate relation (which seems to me) is that temperature is a purely
: thermodynamically defined thing, namely from the Carnot cycle, and the average
: kinetic energy of the system is related to the temperature in classical
: statistical mechanics through the equipartition principle, but this is only
: valid for gas, not valid for liquid or solid.
: For gases, the increase in pressure is purely due to the increase of the
: frequency of collisions of gas molecules with the container, their momenta i
| w********h
发帖数: 12367 | 4
average
sorry for my jumping in because I don't know or understand the problems here.
I think that equipartition principle is vaild for dilute solution.
is that right?
【在 c*****e 的大作中提到】
:
: A more accurate relation (which seems to me) is that temperature is a purely
: thermodynamically defined thing, namely from the Carnot cycle, and the average
: kinetic energy of the system is related to the temperature in classical
: statistical mechanics through the equipartition principle, but this is only
: valid for gas, not valid for liquid or solid.
: For gases, the increase in pressure is purely due to the increase of the
: frequency of collisions of gas molecules with the container, their momenta i
| s*******r
发帖数: 92 | 5 P V
!【 在 chenchuan (work!) 的大作中提到: 】 | c*****e
发帖数: 238 | 6 Well, from Boltzmann statistics, you can easily derive the equipartition
principle, if there is an interaction part which is momenta independent
(e.g. two body potential), then you can not integrate out the momentum part
as they only enter in the hamiltonian as kinetic energy, so the equipartition
principle still holds for kinetic energy. If the interaction
part depends on the momentum, then we can not have the same result.
So I guess you are right. I was misleading.
【在 w********h 的大作中提到】
:
: average
: sorry for my jumping in because I don't know or understand the problems here.
: I think that equipartition principle is vaild for dilute solution.
: is that right?
| c*****e
发帖数: 238 | 7 Well, I guess I was not clear about the relation between average kinetic energy
and temperature. I think the equipartition principle should still be applicable
in weakly interacting system (see my previous post), not for those systems when
the interaction involves momentum/velocity of particles.
For your second question, I think in most liquid, the distance between neighbour
molecules is roughly the equilibrium distance, thus should be attractive, but
you can not squeeze the liquid very much as
【在 c*******n 的大作中提到】
: You got very good points, Thank you very much. I missed the conceptual
: difference between diffusion coeff. and translational energy for the first
: question.
: Actually, equipartition principle is still widely used in the most common
: molecular dynamics software (like insight) to extract temperatures out from
: pure momenta, no matter what substance is, asfar as I know. It seems that
: you mean the temperature can not be regarded as the single function of the
: kinetic energy for liquids, which means the a
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