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Really quick doubt: we know that $\overline{E_c}=\frac32 kT$ where $k=1.38\cdot 10^{-23}\frac{J}{K\cdot particles}$ but particles isn't really a unit, I know, but imagine they ask me about $N$ particles. Would it just be then $E_c=\frac32 kT\cdot N$?

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With the risk of sounding unpurposefully passive-aggresive, the answer is simply:

Yes.

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    $\begingroup$ Which is a reason why "check my work" questions are usually off topic. $\endgroup$ Dec 13, 2020 at 15:04

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