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You have a cup of water that is at equilibrium with the surroundings. that means that equal amounts of water are evaporating and condenses at the same rate. if heat is added to the system what would be the effect?

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If the heat is added to the system then according to Le-Chatelier's principle, equilibrium will shift towards product, that means rate of evaporation will exceed to rate of condensation.
User Akshay Bheda
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