Consider a current flowing through a resistor. Let K_1 and K_2...

When a current flows through a resistor, the applied electric field continuously accelerates the conduction electrons, thereby increasing their kinetic energy.

These energetic electrons undergo frequent collisions with the metal ions in the lattice, transferring a portion of their kinetic energy to the ions. This energy transfer is responsible for the Joule heating of the resistor.

For a continuous net transfer of energy from the conduction electrons to the metal ions, the average kinetic energy of the conduction electrons ($K_1$) must be greater than the average kinetic energy of the metal ions ($K_2$).

Furthermore, according to the quantum free electron model, the average kinetic energy of conduction electrons is determined by the Fermi energy, which is typically of the order of a few electron-volts (eV). In contrast, the average kinetic energy of the metal ions is determined by the thermal energy ($\_approx \dfrac{3}{2}k_BT$), which is only about $0.04$ eV at room temperature.

Therefore, $K_1 > K_2$.