Heating the water makes the water molecules move more. A lot more. So they also break down water-soluble things faster.
Its the same thing with salt or sugar. If you put either in cold water it will dissolve less and slower than if you heat the water.
Steeping tea is dissolving and breaking down various things in the tea leaves. It will steep in cold water…. eventually. And unless the tea is intended for cold steeping its probably not going to be as strong either.
There’s a rule of thumb in chemistry: for every 10 degrees Celsius reaction rates double. It’s not precisely true but it’s in the right ballpark for most things. It also applies to physical changes like dissolution. So going from ~20°c to 100°c would be 8 doublings or ~256x faster.
As to why it’s because the water molecules are moving faster. The stuff that dissolves is moved away from the tea leafs faster which lets more dissolve.
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