Question

No heat is supplied to a liquid during evaporation how does then the liquid change to its vapours

Answer 1

If no heat is supplied then the liquid changes to vapour by the process of evaporation.
Evaporation is a process in which the surface molecules get escaped from the liquid to mixup with air and hence the water level decreases.
The evaporated liquid molecules get mixed with atmosphere and forms humidity in air.

Answer 2

During evaporation, particles of water absorb heat from the surroundings to change their state. The particles at the surface absorb more heat and change into vapour.