Just a quick temperature question!

[brad89]

Just out of curiousity, and I can't seem to find the answer, but if a container of gas was said to be 60 degrees, would every single molecule that makes up the gas be 60 degrees, or would they be, like, 60 degrees divided by the number of molecules that make up the gas, like making a decimal degree that represents each molecule? I hope someone gets what I am trying to say.

 

In a nutshell, does anything that is a certain temperature have molecules that are all that temperature, or does that temperature get divided by the number of molecules that make up the object.

 

Dammit, i can't word it right! Hopefully, one of you understand what I am saying.

[BhavinB]

Temperature is actually a property derived from a large number of particles and it has no meaning for individual particles or a very small number of particles. So the answer to your question is no to both your options.

 

In statistical mechanics, the concept of temperature comes about in a very abstract way. It is sort of related to how a large number of particles are distributed in energy. If you think of all the particles as vibrating, you can say that some are vibrating fast and some vibrating slow. And in some way, this distribution gives rise to what we call as temperature. But it is incorrect to say "what is the temperature of one molecule".

 

B

[aommaster]

...and as a result of that, a Boltzmann curve is produced, right?

[BhavinB]

...and as a result of that, a Boltzmann curve is produced, right?

 

The Maxwell-Boltzmann distribution, yes.

[vrus]

Correct me if I am wrong. Temperature indicates the amount of Kinetic energy possessed by the paticles of the substance in a volume. For example, in a gas, as the particles are always moving randomly (Brownian Motion) they collide with each other and/ or the inner surfaces of their container. If they collide with each other they transfer their kinetic energy, slowing themselves down, but speeding up the one they collided with, so it evens it out and the AVERAGE kinetic energy remains them unless affected by other factors. So you can never really know a molecule's energy as it will change constantly. If you evaporate water, those molecules at the surface requires lesser energy to become vapour than those below it. If quite a few molecules leave the vessel of water, the avergae kinetic energy falls considerably enough and the water's temperature decreases.

[aommaster]

What you said is exactly correct.

 

And therefore, you can work out the average molecular speed of a gas by using the following formula:

[math]

\tfrac{1}{2} <c>^2=\tfrac{3}{2} kT

[/math]

Where:

<c^2> is the mean square speed

k is Boltzmann's constant

T is the temperature of the gas

 

And from that you can see that average speed of the particles is proportional to the tempereature, which you stated earlier!

 

 

Haha! My first Latex equation!