Help with Basic Concepts in Thermodynamics

spartan711

Hi Everyone, quick intro. I am taking thermodynamics (chemical engineering style, college) and am just generally confused by the concepts such as T, U, H, S, fugacity, etc, so I decided to revise my understanding and work my way up from classical physics. and I need some help with that. I will update this post every time a concept is made clear. The way I propose to understand these concepts are simple thought experiments, and then put these concepts in different examples.

1. Temperature (?)

What is temperature? Building on my previous knowledge from high school physics and college physics, the temperature of a molecule is proportional to the translational kinetic energy of the molecule. This does not rotational energy. But does this include vibrational energy? What type of energy does this include if at absolute zero there is supposed to be zero energy (besides quantum)?

2. Energy (?)

Assuming a single molecule flying around in some fixed volume V, how many different forms of energy are present? Assuming no change to the mass, or actual molecule?

Mass energy - mc^2 , Do not consider (DNC)

Bond energy - energy stored in bonds, defined by bond-enthalpy, (DNC) (includes torsional forces)

*I have read in a Material Science Engineering journal that increasing temperature stresses the bonds in molecules. What is the mechanism for this? It was for color changing materials.*

Vibrations of the molecule - defining vibrations as movement from one axis to the opposite axis from the center of the molecule (not intermolecular stretching).

Rotation of the molecule - rotating about the center of mass of the molecule. This is important for atoms, but I am not sure about molecules.

Translational motion - analgous to drift velocity of an electron. Assuming constant velocity, the velocity away from the center of the molecule.

These are all the energies I can think of. Now, of these energies, which contribute to temperature, and which contribute to internal energy? (I am aware of that for an ideal gas, internal energy is a function of temperature, but I am just trying to be as general as possible)

Pressure, enthalpy, and entropy will be followed up as soon I understand the above concepts. Thank you for all your help!

Andrew Mason

Temperature is a measure of the total translational energy of the molecules. For an ideal gas this is fairly straight forward. It does not include rotational or vibrational energy because these do not, overall, move the centre of mass of the molecules or of any two colliding molecules ie. it does not impact average translational energy of the molecules. But for a solid, the vibrational energy of the molecules does affect the translational energy - the motion of the centres of mass of the molecules, since they are all pushing against each other.

AM

spartan711

Thanks for responding AM. I don't think I'm ready to consider liquids and solids yet, as they have intermolecular forces that I haven't really thought about. But your explanation does make sense initially.

So, if temperature is proportional of translational energy, then for our single molecule, its T would be defined as
[tex]
T=(mv^2)/3k
[/tex]

Extending this to many identical molecules (like an ideal gas), the T would be
[tex]
T=(mv^2_{avg})/3k
[/tex]
, where
[tex]
v_{avg}
[/tex]
can be determined from a Boltzmann velocity distribution.

Now, if there were several different molecules (a mixture of ideal gases), the T would be the average of
[tex]
\frac{2*KE_{avg}}{3k}=T
[/tex]
Where the KE of each particle could be calculated with appropriate Boltzmann distribution curves.

Is all the above correct?

For Internal Energy, going back to the one molecule example, what types of energy (from my list) would have to be considered?

be warned: I will soon attempt to understand where blackbody radiation comes from. Although I will probably wait until I fully understand entropy. :)

Andrew Mason

No. T is a statistical concept that requires a large number of particles, all in thermal equilibrium. Temperature of a single molecule is not defined. Temperature is defined by the Maxwell-Boltzmann distribution that a population of particles in thermal equilibrium has. It is the point on that curve (speed v. no.) that divides the area under the curve into two equal parts (equal numbers of molecules with speeds higher and lower).

[itex]<KE_{tr}>_{avg-i} = kT/2[/itex] for each translational degree of freedom. A molecule has 3 translational degrees of freedom, so the total translational average KE is:

[tex]<KE_{tr}>_{avg-total} = 3kT/2[/tex]

This is NOT the total internal energy of the gas. It is the total (internal) translational kinetic energy.

AM