why is heat absorbed from our body during perspiration equal to latent heat of vapourisation
When water turns to gas, it absorbs heat from its surroundings and this is called the latent heat of vaporization. On a humid day, the air is almost saturated, so the sweat tends to cling to the body (as heat is absorbed by our body). Sweat (perspiration) is most effective in dry heat, as is evaporative air conditioning.
The way in which water cools down a hot pan, water absorbs heat and evaporates thus causing your body to cool down. It is the evaporation of the sweat on the surface of our skin that creates the cooling effect. As the heat is required to convert moisture into a vapour, the heat is supplied by the body (latent heat of vaporization) via the skin to convert the sweat to vapour and this loss of heat is felt as cooling.
Hence heat absorbed from our body during perspiration is equal to latent heat of vaporization.