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Why spraying causes cooling if the work is not done by an external force then internal energy of liquid decreases subsequently temperature decreases.

but in a a spray bottle we apply external mechanical force????

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Spraying water into a fine mist causes a cooling effect by evaporation of water from the droplet surfaces. The lower the relative humidity of the surrounding air, the finer the mist, and the colder the water being sprayed, the greater the cooling effect.

This is called evaporative cooling and a full description can be found in any heating/ventilating/air-conditioning (HVAC) textbook under the heading of airwash systems.

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