### The Science of Paella

#### Overview of the Science

• Heat is limited by random collisions between the molecules in the food, a process called diffusion.
• Faster moving molecules transfer their energy to slower moving molecules, so differences in temperature are decreased.
• Foods cook faster if the external temperature is higher.
• The temperature rise is fastest at the start of cooking, then slows down as the temperature of the food approaches the final temperature.

#### Equation of the Week

###### How fast does heat flow into food?
• The cooking times of most foods are limited by the diffusion constant, D, of water.
• The average distance, L, traveled by diffusing molecules (or heat), is related to the time, t, by:

$$L = \sqrt{D t}$$

• In theory, if the size of a food is doubled, then the cooking time increases by closer to a factor of four. Heat travels faster than other types of diffusion, so brining or soaking is often the most time-consuming step in a recipe:
##### Making perfect caramelized onions takes several hours

Below is a series of photos of onions at different stages of browning:

You can find out more about browning reactions in Week XX

#### Beyond the Lecture

###### The mathematics of sous vide cooking

Applied mathematician and sous vide expert Douglas Baldwin gives a nice introduction into the mathematics of sous vide in his book.