Is tea weaker if you make it in a half full cup of water? Imagine you put a tea bag in a cup and half fill it with boiling water. Then after one minute you take the tea bag out and then fill the cup up to fill with hot water.  Will the tea be weaker than if you had filled the water up to the normal level with boiling water in the first place and then left it for one minute before taking the tea bag out?
Intuitively I can make an argument that it should be but is there a mathematical description for how much weaker it would be?
 A: In answer to your question - the math you seek is somewhere in the Noyes-Whitney equation as pointed out in the following link analysis of teabag dynamics unfortunately the author doesn't expressly calculate the rate of dissolution but the ammount of detail will either A/ give you a good start on figuring it out - or B/ help you decide you don't need to know the exact answer that bad.
My take on it is that the rate of dissolution starts the same in both cases and the value for the bulk mass concentration [Cb] will increase faster for the half cup slowing its dissolution rate faster.
To determin a definative answer you would need to integrate the rate of dissolution for both cups to find out the total ammount of tea compounds delivered into the water on your calculator.
My gut says that brewing in the full cup will be stronger. 
A: Each substance in the tea leaves will have a certain maximum soluble concentration in water.
If there are enough tea leaves in the bag to reach saturation of a full cup of water for a given compound, then for half a cup only half as much of that compound will dissolve.
For a compound that doesn't reach the saturation point even for half a cup of water, there may be no difference.
So it is not simply that the tea will be weaker.  The ratios of the compounds in the tea solution will also be different.
