Richardson-Dushman Equation

The vacuum tube consists of anode, hot cathode sealed in a glass tube. The current density between anode and cathode determined by following equation: 

$$j=A\cdot T^2{e}^{-\frac{W_a}{kT}}$$

Here, $j$ is density of current of thermionic electrons.  $T$ is temperature of hot cathode, k is constant of the Boltzmann, $W_a$ is work needed to extract an electron from the metal.