Time (s)	Description
0:00 - 0:07	Our lab instructor Matt Smith shows two beakers: one at 4.3°C, the other at 66.1°C.
0:07-2:29	Time lapse shots of the dye diffusing. The blue dye is in the cold water, and diffuses slower because the average speed of the molecules is slower.

What is going on?

Recall from 7A that the energy per mode is ½k_BT. The olecules all have three translational kinetic modes:
Average KE per molecule = 3 × (½ k_B T) = ½ m v²_ave

Therefore the average speed is related to the temperature in the following way:
v_ave = (3 k_B T / m)^½
The hotter it is, the faster the molecules are going!

The dye is carried out by colliding with the water molecules. The water has (roughly) the same density at these two different temperatures, so the distance between collisions is roughly the same. Because the water molecules are travelling faster in the hotter water, the dye tends to move faster. In a hotter environment, diffusion occurs quicker. That is why the green dye spreads out faster.

Extra comment

You may worry that I am playing a trick on you - are you absolutely sure that the substances in the green food colouring are the same size as the substances in the blue food colouring? Swapping the two food colourings produces the same result &emdash; the food dye in the hotter water diffuses faster.

The reason for the choice of colours was purely an aethstetic one: I used blue for cold!