Write the unit and dimension of the Boltzmann constant.

(N/A) The Boltzmann constant $(k_B)$ relates the average kinetic energy of particles in a gas to the thermodynamic temperature of the gas.
It is defined by the equation: $PV = N k_B T$,where $P$ is pressure,$V$ is volume,$N$ is the number of particles,and $T$ is temperature.
Rearranging for $k_B$: $k_B = \frac{PV}{NT}$.
The unit of pressure $(P)$ is $Pascal$ ($Pa$ or $J/m^3$),volume $(V)$ is $m^3$,and temperature $(T)$ is $Kelvin$ $(K)$.
Thus,the $SI$ unit of $k_B$ is $\frac{J}{K}$ (Joule per Kelvin).
To find the dimension,we use the formula for energy: $Energy = Force \times Displacement = [M L T^{-2}] \times [L] = [M L^2 T^{-2}]$.
Since $k_B = \frac{Energy}{Temperature}$,the dimension is $\frac{[M L^2 T^{-2}]}{[K]} = [M L^2 T^{-2} K^{-1}]$.