Why does microwave take more time to heat more food?

Question

As I understand, a microwave works by generating an electromagnetic field. As food enters this field, waves will transfer energy to those food particles that are intercepted by waves, and those particles that are not intercepted by waves will not be heated. On the other hand, there will be empty regions without food, that are receiving waves that could potentially transfer heat if something was there. So eventually, if food is added to the microwave it will receive these waves that were directed to empty space before. I think that, in first case where this region was empty, waves didn't transfer any energy. And in second case, when a body is added, they will transfer heat to the body.

Answer 1

The microwave transfers a certain amount of energy per time. This is known as the power $P$, and is what you set when choosing how many watts you want: $1\mathrm{W} = 1\mathrm{J}\cdot \mathrm{s}^{-1}$.

The food absorbs a certain amount of energy per mass. The amount of energy per mass needed to raise the temperature by one unit is known as the specific heat capacity $c$, which has units of $\mathrm{J}\cdot\mathrm{kg}^{-1}\cdot\mathrm{K}^{-1}$. Now we write $P=\frac{E}{t}$ as well as $c = \frac{E}{mT}$ and rearrange terms to find $$ t = \frac{mcT}{P} $$from which we can conclude that the time needed to heat the food depends linearly on the mass of the food.

EDIT: It should be noted that this is a purely phenomenological explanation (Which is appropiate for a phenomenological question, but still). In general, the specific heat capacity depends on the temperature, and all quotients are indeed differentials, so that the time would be given by an integral.

Answer 2

There are several factors that time it takes the food to heat up.

• Heat takes time to diffuse into the food and if there is more food the depth to which the heat has to diffuse may be larger.
• Microwave ovens are power limited and it takes more power to heat a larger amount of food in the same time. In the presence of a larger load the field will be less intense at the same power.
• The efficiency of the microwave oven to generate a field may go down with the oven filling factor.

Answer 3

This is an excellent opportunity to do an experiment in your kitchen! Don't just take our word for it - design an experiment and find out!

More food means more particles to heat. You're increasing the amount of work the oven has to do, but you're not increasing how much power it uses to do so - the wave still has the same energy, E=hf, where the frequency is on the microwave band. So in order to do more work with the same power, you have to do it for a longer time. It's the same reason it takes longer to boil a big pot of water than a small one. The rate of heat transfer remains constant, but the amount of heat that NEEDS to be transferred is much higher.

By the way, microwave ovens don't actually heat food. (At least, not directly - food obviously does come out hotter, after all.) Microwave ovens actually heat water, because the specific microwave frequency used in the oven is the same as the resonant frequency of water. When the water interacts with a wave at its resonant frequency it shakes back and forth faster and faster, like a kid on a swing set who get pushed every time they get to the top. This greatly increases the kinetic energy of the water molecules, which is then transfered to the food molecules all around it, heating the whole thing up. It works so well because there's lots of water in basically all food, but you might notice it works less well for dry foods. If you've ever put your hand in a microwave oven afterward and felt it full of hot steam while the food was still cold, that's why. (It gets more complex than this - like another user mentioned, it also depends on how dense the food is, and how capable the food is of absorbing/transmitting microwaves into its interior. Ice crystals also don't have the same reasonant frequency. Some food materials will reflect the microwaves, and prevent them from penetrating - leading to frozen insides but burnt outsides. TV diner trays often have microwave-reflective bottoms to keep the wave in the food.) Try microwaving a cup of water and see how long it takes to get hot for different sizes. Do some experiments microwaving different things.

A third thing to note is that microwave ovens create standing waves. Everywhere a node of the standing waves forms, the heat transfer will be zero. You can see where these are by taking a paper towel, dipping it in water, and microwaving it. You should see a pattern form that shows you where the nodes are - they'll be where the towel is still wet.

Answer 4

Perhaps worth adding to the answers above that food is not transparent to microwaves - in fact, it is absorbing them (which is why it is heated). Thus, the intensity of the microwave incident on an object inside decreases with depth $d$ approximately as $\propto e^{-\alpha d}$. In other words, the food is not heated uniformly along all of its volume, but only at the surface - although the heated layer is much thicker than that for an object in contact with a hot pan.

In fact, it is a common observation that an object coming out from a microwave may be hot outside, but still cold inside (in my experience, most noticeable with bread taken out of freezer.)

The heat from the surface propagates via heat conduction, as pointed out in the answer by @paulina.

Note also that more transparent objects take longer time to heat - notably soups and other water-based products... although I might be wrong and it may have to do with higher heat capacity.

Related: Why does evenly heating soup with a microwave take so long?

Answer 5

So eventually, if food is added to the microwave it will receive these waves that were directed to empty space before. I think that, in first case where this region was empty, waves didn't transfer any energy. And in second case, when a body is added, they will transfer heat to the body.

Waves in a microwave oven aren't "directed to empty space". A microwave oven basically "pushes" microwave energy into the oven, where it bounces around until it's absorbed by something. Modern ovens are designed to maximize the chance that this bouncing will intersect the food.

This means that no matter how much or how little food you put in the oven, all of the energy coming out of the emitter gets absorbed by it. If you put in twice as much food, you need twice as much energy to heat it by the same amount, which means twice as much time.

If the oven is completely empty, the only available "something" for absorbing energy is the microwave emitter itself (the same design that makes for a good emitter also makes for a good absorber), which heats up and may catch fire or explode.