Sugar is highly soluble in water. At room temperature (20 degrees Celsius), 100 ml of water can dissolve as much as 204 gm of sugar. A tablespoon holds about 10-15 grams of sugar (depending on how much sugar you can get into it safely).
Thus, all the sugar in a tablespoon will easily dissolve in 500 ml of water (unless the water is frozen), since sugar has high solubility in water. One may need to mix it with a teaspoon or tablespoon, though.
We can also increase the solubility further by heating the water. As the temperature of water goes up, its ability to dissolve things like sugar and salt increases. As the water cools down, the extra sugar (beyond the saturation limit at that temperature) separates out of the solution. One can observe this through a simple experiment at home.
Hope this helps.
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