Solubility can be thought of as the maximum amount of a solute that can dissolve in a solvent, at equilibrium. Remember that a solute is a substance that is dissolved, while solvent is a substance in which the dissolution takes place.
Since solubility is the upper limit, it cannot be increased by stirring the solution or by adding more solute. Stirring the solution will simply increase the rate of dissolution, but not the maximum amount of solute that can be dissolved. Stirring spreads the solute uniformly in a solvent and increases the number of interactions between solute and solvent molecules. This causes a higher rate of dissolution. That is why we stir hot tea after adding sugar to it. Increasing the amount of solute, beyond the solubility limit, will not help and all the extra solute will be left out of the solution. Another method to increase the rate of mixing is by providing increasing the surface area of the solute, say by grinding or crushing it into smaller fragments.
It is the temperature that affects the solubility of a solute in a solvent. With an increase in temperature, more solute can be dissolved in the solvent.
Hope this helps.
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