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.