The question is: when two bodies with the same thermal conditions, is the average kinetic energies in those two bodies the same? The answer is their temperature is the same. And recall that their average kinetic energies isn't the same. I'm not very understand about this, I wonder to get an answer. What in my mind is the total average kinetic energy of all the particles inside a body is directly proportional to its temperature, so I think if two bodies have the same thermal conditions, then their average kinetic energies as well as temperature are both the same. Anything wrong in my above sentences?

The question is: when two bodies with the same thermal conditions, is the average kinetic energies in those two bodies the same? The answer is their temperature is the same. And recall that their average kinetic energies isn't the same. I'm not very understand about this, I wonder to get an answer. What in my mind is the total average kinetic energy of all the particles inside a body is directly proportional to its temperature, so I think if two bodies have the same thermal conditions, then their average kinetic energies as well as temperature are both the same. Anything wrong in my above sentences?

 

Overall it's OK, but: It is important to note that it is the average KE - statements like "total average KE" are potential hazards, as they contain a contradiction.

 

Same temp = same average KE

Then, you mean they have the same average KE?

Temperature is a measure for energy distribution. For classical ideal gases that do not have any particle interaction I can very well imagine that equal temperature directly translates to equal energy distributions and therefore equal average kinetic energies.

I do not think that "equal temperature = equal average KE" still holds true for more complex systems with particle interactions and bound states.

 

A rather (although quantum mechanical and therefore probably leading beyond the homework scope) radical example of two systems with equal temperature and nonequal kinetic energy would be the free bosonic gas and the free fermionic gas in the limit of temperature -> 0.

Temperature is a measure for energy distribution. For classical ideal gases that do not have any particle interaction I can very well imagine that equal temperature directly translates to equal energy distributions and therefore equal average kinetic energies.

I do not think that "equal temperature = equal average KE" still holds true for more complex systems with particle interactions and bound states.

 

A rather (although quantum mechanical and therefore probably leading beyond the homework scope) radical example of two systems with equal temperature and nonequal kinetic energy would be the free bosonic gas and the free fermionic gas in the limit of temperature -> 0.

 

I think for the OP we're firmly in the idealized world of textbook examples.