Which property of water allows dogs to cool themselves by panting?

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latent heat of Vaporisation.

Explanation:

This is the  quantity of heat energy needed to change a specific  amount of water to vapour

The strong hydrogen  bond  in   water held its molecules tightly.Therefore for the molecules to be freed, to vapour energy must be supplied from the environment to breakdown the hydrogen bonds.The withdrawal of this energy from the environment  lowers the heat in the body for evaporation  to occur.  

In dog undergoing panting,  as the  inhaled humid air passes over the mucous membrane it trapped heat  in the tissues .The moisture is transported to the tongue where it is evaporated to vapour by drawing heat from the tongue.

Since evaporation brings cooling effect,  by drawing heat energy  from the tongue, using latent heat of vaporization,  it cools off the body of Dogs.

the missing space is phylum