Kinetic Temperaturea and molecular velocities

[mrcotton]

If I have ice, water and vapour at the triple point and they are in equilibrium at a temperature of 273.16. Does this mean that the average kinetic energy of the particles is the same in each state? If so how can the molecules in the water be moving with the same mean squared speed as the molecules in the vapour? Thanks for any help

 

[Matterwave]

At the triple point, it is not he kinetic energies which are equal, but the chemical potentials $\mu$ of the 3 phases of matter.

 

[mrcotton]

Thanks for responding Matterwave

Where this question has come from is a discussion I was having about temperature increase as water changes from the solid to the gaseous state. As the water changes from D to E, If temperature is defined as average KE =3/2kT does this imply that the KE and hence the translational mean squared speeds of the liquid at D and the gas at E are the same if they are at the same temperature?

 

[vjacheslav]

Does kinetic temperature real because of molecular moving?
Hint: something else moving?

 

[sardar]

Yes, at the triple point, the average kinetic energy of the particles in ice, water, and vapor is the same. This is because at this point, all three states are in equilibrium and have reached a state of thermal equilibrium, meaning there is no net transfer of heat between the three states.

The kinetic temperature of a substance is a measure of the average kinetic energy of its particles. At the triple point, the kinetic temperature of all three states is the same, indicating that the average kinetic energy of the particles is also the same.

However, this does not mean that the molecules in water and vapor are moving at the same mean squared speed. The mean squared speed is a measure of the average speed of the particles, and it is affected by the mass of the particles. While the average kinetic energy may be the same, the mass of the particles in water and vapor is different, resulting in different mean squared speeds.

Additionally, the kinetic energy of individual molecules can vary within a substance, even at the same temperature. This is due to the distribution of molecular velocities, as some molecules may have higher or lower velocities than the average.

Overall, the triple point and its equilibrium state only indicate that the average kinetic energy of the particles is the same, not the mean squared speed or the individual kinetic energies of the molecules.