# In a microwave oven, why do smaller portions heat up faster?

The magnetron injects microwave radiation at a certain rate. Ignoring losses, that radiation bounces around the walls until it’s absorbed by the food. If you put two burritos in there instead of one, on average there will be fewer bounces before absorption. That means that with two burritos, the average intensity of the radiation impinging on any point is less—some of photons, if you want to think of it that way, that would have been hitting the spot aren’t there because they’ve already been absorbed.

This is quite different from a regular oven—as long as there is enough power to keep the air temperature at the desired setting, it doesn’t much matter how many burritos you put in there, as long as there’s air space between them. They are heated by conduction from the air, which is unaffected by neighbors, and blackbody radiation from the surroundings which is only affected a bit.

Let $$P$$ be the power (in $$\mathrm{Watt}$$) the microwave delivers then a simple heating model can be stated as follows.

The heat energy $$q$$ needed to heat an object is:

$$q=\varepsilon mc_p\Delta T$$

where $$\varepsilon$$ is an efficiency factor (for food stuffs with a high moisture/water content $$\varepsilon \approx 0.9 - 1$$). $$m$$ is the mass of the object, $$c_p$$ its specific heat capacity and $$\Delta T$$ its rise in temperature on heating.

Because:

$$P=\frac{\mathrm{d}Q}{\rm{d}t}$$

It can then be shown with minimal calculus that the heating time $$\Delta t$$ is given by:

$$\Delta t=\frac{\varepsilon mc_p\Delta T}{P}$$

So all other things being equal (same composition, same $$\Delta T$$), objects of smaller mass $$m$$ require smaller heating times.

Microwaves do not fill the microwave cabinet uniformly. They form a "standing wave pattern" with high-intensity and low-intensity regions. When something is placed in the cabinet, it distorts the standing wave pattern, so the pattern of hot and less-hot portions can change. The reason most microwave ovens include a rotating turntable is to attempt to "blur out" the exposure of different parts of the thing being cooked so the heating is more uniform.