The energy change would you expect to take place in the molecules of a substance when it undergoes a change in its state without any change in its temperature is
increase in Potential energy
When the heat supplied causes no change in the temperature of the substance, the heat supplied to the substance is utilised to change the state by separating the molecules and overcoming intermolecular forces of attractions. This change increases the Potential Energy of the molecules. This heat absorbed is called Latent Heat.