Question

water stored in an earthen vessel become cool

Answer 1

because walls of earhern vessel is porous in whch water can pass throught it t. in this case the water stored in earthern vessel passes to an exposed surace and hence rate of evaporation is more in more exposed surface .
as you know that the evaporation causes cooling,if the rate of of evaporation is more the water inside earthern vessel becomes more cooler

this is the reason that the water kept in earthen vessel cools faster
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Answer 2

Water looses its temperature through small pores present in the pot. Hence in an earthen pot (matka) become cool during summer.