# Temperature and kinetic energy of molecules

I was wondering if temperature is related to the average translational kinetic energy of the molecules then why does the average kinetic energy of say a moving object not affect the temperature? What is the mechanism regarding these vibrational motions that imparts temperature. Also do a gas and liquid at the same temperature possess the same kinetic energy? and a heavier molecule traveling at the same speed as a lighter molecule will have a greater temperature?

• "What is the mechanism regarding these vibrational motions that imparts temperature". Can you be more specific on what you're asking? – Bob D Dec 22 '19 at 23:02

I was wondering if temperature is related to the average translational kinetic energy of the molecules

Yes temperature is related to the average translational kinetic energy of the molecules (technically called its kinetic temperature), or its internal translational kinetic energy.

then why does the average kinetic energy of say a moving object not affect the temperature?

Because the average translational kinetic energy (measured by temperature) of the contents of the system is the internal kinetic energy of the system, whereas the translational kinetic energy of the center of mass of the system as a whole is the external kinetic energy of the system, i.e., its kinetic energy with respect to an external (to the system) frame of reference, such as the room reference frame where the object is located. The motion of the center of mass of the object does not effect its temperature because temperature is caused by the random motion of the atoms and molecules of the object. That random motion is not altered by the collective motion of the center of mass of the object.

What is the mechanism regarding these vibrational motions that imparts temperature.

It is not "vibrational motions" that is associated with temperature. It is, as you have already noted, translational motions that are associated with temperature. Taking a gas as an example, the greater the average translational kinetic energy of the gas molecules, the greater the number of collisions per unit time between the molecules themselves and any surfaces they contact. If, for example, a glass bulb thermometer is placed in the container, collisions of the gas molecules with the glass transfers kinetic energy from the gas into the fluid in the thermometer. That causes the thermometer fluid to expand and rise in the thermometer tube, providing a temperature reading.

Also do a gas and liquid at the same temperature possess the same kinetic energy?

They posses the same average translational kinetic energy, since that is what temperature measures. But there are also vibrational and rotational kinetic energies of molecules that may be different for the gas and liquid and that are not associated with the temperature of the gas and liquid.

and a heavier molecule traveling at the same speed as a lighter molecule will have a greater temperature?

First of all, temperature is generally considered a macroscopic property of the system, i.e. individual molecules are generally not considered to have a temperature. That said, a heavier molecule (molecule of greater mass) traveling at the same speed as a lighter molecule (molecule of lesser mass) will have a greater kinetic energy since kinetic energy is $$\frac{mv^2}{2}$$.

Hope this helps.

• Of course, rotational and vibrational kinetic energies are also associated with temperature. In a liquid, it is difficult to distinguish them from translational kinetic energy. And it is only in the classical approximation that kinetic energy is measured by temperature. – user137289 Dec 23 '19 at 0:06

This link will help s will the image :

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Temperature is a thermodynamic variable, i.e. at the atomic and molecular level it has to do with the kinetic energy of the atoms/molecules/lattices , whose average can be shown to be connected to the thermodynamic temperature.

For an ideal gas :

why does the average kinetic energy of say a moving object not affect the temperature

Because it is at the rest frame of the objects that temperature is defined. The overall motion makes no difference. ( Are you hotter when moving with 60 miles an hour?)

What is the mechanism regarding these vibrational motions that imparts temperature.

Molecules can contain extra motions , as seen in the link, and this can add extra complication in the statistical estimate. Usually temperature goes by the thermodynamic definition.

As quantum mechanics is the framework for correct estimates at the microscopic level, the QM energy levels of vibration and rotation have to be taken into account,as well as the scatterings and radiation due to the inherent charges in the material. This leads to black body radiation which is specific to the temperature of the sample, but that is another story.

As temperature can be equated with an average kinetic energy, if the kinetic energy of a molecule is measured, one could say that it corresponds to the average kinetic energy of temperature T, but it has no meaning to say that a molecule has temperature, as to get thermodynamics one needs a large number of molecules.

• Temperature is not defined as average kinetic energy. Only in the classical approximation are these quantities proportional to each other. – user137289 Dec 23 '19 at 9:43
• @Pieter I do not disagree, Temperature is a thermodynamic variable. to start with.. I removed the "defined" – anna v Dec 23 '19 at 12:16