Why energy at room temperature $= kT$ and not $(3/2)kT$ I always see that a room temperature of $T=300\,\text{K}$ corresponds to an energy of $k_BT \approx \frac{1}{40}\,\text{eV}$. But shouldn't it be $\frac{3}{2}k_BT$ since the molecules in the air have three degrees of freedom for translation and not two? Is there a deeper meaning to neglect the $3/2$?
 A: Giving the value simply of $k_B T$ is generally more useful, because I can plug that into anything. Sure, I might need to know the ideal gas energy, and multiply by $3/2$. But maybe I need to put it into a partition function, and I just need $k_B T$. Maybe I'm worried about a harmonic oscillator and I just have the two degrees of freedom. The 3/2 is appropriate for a very specific quantity, but $k_B T$ shows up everywhere. In addition, I suspect often when you hear this someone is trying to make a point about what scale of energy we should be talking about, and in this case the 1.5 is not so important. I just want to know if we're talking $eV$, $MeV$, $meV$...
A: The thermal energy $k_{B} T$ is really referring to the probability of finding a system in a state of energy $E$, given that it is in a surrounding enviroment at temperature $T$. This probability is proportional to $e^{-E/(k_{B} T)}$. Using this you can derive a great many things, including the Boltzmann/Fermi distributions. 
The proportionality constant is $1/Z$, where $Z=\sum \limits_{s} e^{-E_{s}/(k_{b} T)}$ is the partition function (summing over all possible states $s$). It's easy to see that the partition function normalizes things so that the sum of probabilities of all states is 1.
