I have so far derived that $$E_K= \frac{3k_BT}{2} $$ where $E_K$ stands for the average random kinetic energy possessed by particles of an average gas. Now we can take one step further by using this result to compute the Internal Energy of an ideal gas. From the assumptions of an Ideal Gas, we know that there is no potential energy between particles and so the Internal Energy is purely composed of random kinetic energy. The author of my textbook goes on to write:

Suppose that the gas has N molecules. Then since the average kinetic energy is $E_K= \frac{3k_BT}{2} $ the total Internal Energy is $$U= \frac{3Nk_BT}{2} $$

I don't understand why is N multiplied to $E_K$ shouldn't $E_K=U$ ?


1 Answer 1


The internal energy is the sum of the energies of all the molecules and $E_k$ is the average kinetic energy for one molecule.


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