|MadSci Network: Biochemistry|
Apples (as well as many other fruits) contain an enzyme known as tyrosinase (often called polyphenoloxidase). This enzyme catalyzes the reaction of oxygen with phenols (hydroxyaromatic compounds), causing the familiar brown color on the cut surface of the fruit. Since the enzyme is only a catalyst, it doesn't act by itself. It merely hastens the reaction of the phenols in the fruit with oxygen in the air.
If the fruit is crushed, the surface area of the "meat" is increased dramatically, and many more of the phenols are brought into contact with the air. On the other hand, if you submerge the fruit, you are keeping oxygen away from it, and the reaction will not take place.
And since there is a chemical reaction involved, yes, temperature will affect its rate. If the temperature is raised too far, though, the enzyme itself may be destroyed. This is why a cook will blanche an apple (dunk it into boiling water): with the enzyme out of action, the phenols will react much, much more slowly with oxygen.
As for measuring surface areas, I don't think that will demonstrate very clearly that this is a reaction with oxygen. A much better demonstration would be to place one apple into each of three plastic bags, one filled with nitrogen or argon, one filled with air, and one filled with oxygen. One should see very clearly that the amount of oxygen available affects the rate of browning.
An old trick that picnickers use is to treat sliced apples with lemon juice. This is because the enzyme's action is inhibited at very low pH. It would be very interesting to dip apple slices into water solutions of differing pH (perhaps 1, 2, 4, 7, 9, and 12) and observing the rate at which they turn brown.
There are some references listed in the Merck Index, 11th edition, under "Tyrosinase" (#9746) that would be of help to you. I suggest also finding a textbook on biochemistry and investigating the mathematics of enzyme kinetics.
Try the links in the MadSci Library for more information on Biochemistry.