Answer to old chestnut: water and wine
There is the same amount of water in the wine as there is wine in the water.
To understand this, let X equal the volume of water in the wine and Y the
volume of wine in the water. Since it is a closed system, we must have
1 gallon - Y wine in the wine and 1 gallon - X water in the water. However,
the total volume in each container is still one gallon, since we removed a
teaspoon and added a teaspoon to each container. So 1 gallon - Y + X =
1 gallon, so Y = X.
This type of analysis is at the heart of material and energy balances,
the first distinctly chemical engineering course most chemical engineering
students take. The calculation above is a material balance on one container,
accounting for all the flows in and out of the container and the initial and
final contents of the container.