[kapital]

Why can molecules accept only quantitated energy(photons), but can have any temperature(can accept any amount of heat ot have any temperature?

Why have molecules continous spectra?(assuming one photon with specific wavelength and energy produce single specific electronic transition, so it woud be logical that absorb only specific wavelengt or few of them)

[Enthalpy]

Some modes are discrete, like electronic levels or vibration modes.
Some are continuous, like the translation of a molecule in an unlimited volume.

And some modes would be discrete BUT are so plentiful that we can't separate them, like translations in a limited but macroscopic volume.

One other reason is when modes have a short duration. Typically rotation modes, which correspond to faint frequency differences (high GHz, THz, far IR). Shocks between molecules stop the previous rotation mode and begin a new one. To observe the modes separately, you need enough observation time (Heisenberg or Fourier, depending on your background) so your frequency selectivity is better than the frequency separation of the modes. If not, too broad and close frequencies overlap, resulting as a continuum for the observer.

So you can observe rotations in a very low-pressure gas, for instance in radio-astronomy. In a liquid, shocks happen too often, and you get a continuum.

-----

With these overlapping modes, you get a continuous temperature scale in a first way.

But there is more. Temperature also tells the probability to get a molecule in some state (Boltzmann and the others), so even states are well separated (vibration of O₂ at RT) a statistics over many molecules gives a temperature. 10.001% in the excited state is warmer than 10.000%.

This is not just a matter of definition and measurement. If you put to pieces of matter in contact and allow them to get in thermal equilibrium, one with well-separated states will really get its statistics to match the other's temperature.

[juanrga]

Why can molecules accept only quantitated energy(photons), but can have any temperature(can accept any amount of heat ot have any temperature?

Why have molecules continous spectra?(assuming one photon with specific wavelength and energy produce single specific electronic transition, so it woud be logical that absorb only specific wavelengt or few of them)

Temperature and heat are quantized as well. What happens is that, usually, molecules are immersed in heat baths and heat baths are large quantum systems with a (quasi)continuous spectra. Moreover kinetic energy has a (quasi)continuous spectra as well. Therefore, molecules can receive/emit infinitesimal amounts of heat and change their speed by the same amount.

[kapital]

Ok. What abaut, when we talk in organic chemistry, that some atoms are more electronegative and thay pull electrons a litle bit closer to them,  and also when we talk abaut resosnance, we are saying that that it goes just changing position of electrons.

How can electrons move like that?

[Mitch]

Temperature is most certainly not quantized. Temperature is an effect that is only meaningfully measured for a large assembly of atoms.

[kapital]

Temperature is most certainly not quantized. Temperature is an effect that is only meaningfully measured for a large assembly of atoms.

Hm. So you cant messure temerature of one atom or one molecule?(in theory)
 

[juanrga]

A basic quantum approach to temperature is given in section "II. TEMPERATURE OPERATOR AND ITS EIGENVALUES" of this recent paper

http://pre.aps.org/abstract/PRE/v54/i5/p4607_1

The equation (27) defines, as they write, "the quanta of temperature".

Temperature is well-defined for small systems. I am not familiar with methods of measuring, but this paper

http://dx.doi.org/10.1051/jp4:2004116007

discusses methods for measuring "the temperature of a single atom in the trap with a high accuracy".

[Mitch]

I'm going to stress the word "meaningful". However, there are many scientists that claim to measure a temperature for a single atom using some theory or approximation. I remember I described a high energy particle as having a temperature by extrapolating what the temperature would be using the equations in the kinetic theory of gasses. So I will say that you could in theory come up with many ways to measure temperature for a single atom, that do not violate other theories, but it isn't a meaningful description of a single atom.

[juanrga]

The 'application' of the kinetic theory of gases (which is only valid for systems with a large number of molecules) to a single atom is not something that I would consider "meaningful", because that is a gross misapplication of a theory beyond its scope.

For small systems one would apply the corresponding thermodynamics of small systems, evidently. Disciplines as nanothermodynamics and quantum thermodynamics are used in the labs for the explanation of the observed phenomena and for the prediction of new observations at small scales. For instance, the thermodynamics of small systems predicted phenomena for nuclei, which were latter observed.

I finally want to emphasize that quantum thermodynamics applies to experimental situations beyond the Schrödinger equation of quantum mechanics.

[kapital]

 Ok.What about continuous spectra of molecules?

[juanrga]

Ok.What about continuous spectra of molecules?

Answered in #2

[kapital]

And some modes would be discrete BUT are so plentiful that we can't separate them, like translations in a limited but macroscopic volume.

Is that what you meant?

[juanrga]

And some modes would be discrete BUT are so plentiful that we can't separate them, like translations in a limited but macroscopic volume.

Is that what you meant?

A continuum spectra is a limiting case when the difference between two levels can be infinitesimal. Electronic, rotational spin... spectra are clearly discrete for molecules because the difference is finite. For translations the spectra is continuous, i.e. the difference between to energy levels can be infinitesimal as the Schrödinger equation shows.

A heat bath is defined as a quantum system with continuous spectra. Therefore a molecule immerse in a heat bath can accept/emit infinitesimal amounts of energy.