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They say that the vibrational kinetic energy is a measure of temperature. Temperature is also related to the entropy as the partial differential. It is a measure of the energy of the atoms within but which types of energy? Say hydrogen bonding increases with a decrease in temperature not the other way around. Which types of energy other than kinetic of the molecules increase with temperature including bonds? How heat transfer between the molecules with temperature difference but not with actual motion? Though actual motion collisions can result in an increase in temperature from stress for example

ChemEng
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  • The answers to the example in this question illustrates the difference between thermodynamic definition and the statistical https://physics.stackexchange.com/q/548965/ . it may help. – anna v May 12 '20 at 04:14
  • Yes but i believe $$ T_{\text{kinetic}}=\frac{2}{3k}\left[\overline{\frac 1 2 m v^2}\right]=\frac{2}{3k}\text{KE}_{\text{average}} $$ is true only for monoatomic ideal gases and there is no real explanation for how heat transfer occurs on the molecular level. How can we derive the thermal conductivity/specific heat capacity from molecular properties? Also as Temperature is the partial of the internal energy wrt entropy then using the Sackur-Tetrode eqn we get the above formula but there are additional concerns for diatomic molecules – ChemEng May 12 '20 at 23:23
  • https://www.quora.com/Is-there-a-Sackur-Tetrode-equation-for-non-monatomic-gases you can see but what are the physical forces that they are talking about? – ChemEng May 12 '20 at 23:24
  • The thermal energy is the sum of the vibrational, rotational and kinetic energies – ChemEng May 13 '20 at 00:11
  • for specific heat see https://farside.ph.utexas.edu/teaching/sm1/Thermal.pdf page 143 or so. again it is only in ideal gases. But it is enough to prove mathematically that the thermodynamic quantity arises from the statistical behavior. Then one uses the simple thermodynamic formulae. for forces, rmember that dp/dt is the definition of force. – anna v May 13 '20 at 03:41
  • yes but if the thermal energy is the sum of the vibrational, rotational and kinetic energies of the molecules then why is the thermal conductivity related to the electrical conductivity – ChemEng May 14 '20 at 18:37
  • I would guess it happens when the electrons are the main carriers. found this https://www.doitpoms.ac.uk/tlplib/thermal_electrical/printall.php – anna v May 14 '20 at 18:48
  • ahh i guess this is how the thermal hall effect and thermocouples work – ChemEng May 14 '20 at 19:06

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