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Question 14: When two systems are in thermal contact, do they have the same amount of kinetic energy?


Suppose two bodies are at different temperatures and they are brought in thermal contact to one another. Heat will flow from the body at higher temperature to the body at lower temperature. A stage will reach when both bodies would have the same temperature. Same temperature means the average kinetic energy of molecules in both bodies will be the same. Suppose, this average kinetic energy (which the molecules of both systems has) is k.

Now, if the number of molecules in one system is 100 and that in the other system is 200, then we calculate the kinetic energies of both systems as follow;
Kinetic energy of first system = kinetic energy of all 100 molecules in this system = 100k
Kinetic energy of the second system = kinetic energy of all 200 molecules in this system = 200k
It is clear that the kinetic energy in the second system is double as the kinetic energy in the first system. So in the state of thermal equilibrium, the systems have same average kinetic energy (= temperature) but the total kinetic energy is greater in the system having larger number of molecules. This means the average kinetic energy per molecule is the same but different systems have different number of molecules, so the total amount (added for all molecules) is different in different systems.

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