Is a microwave's output power proportional to the mass of its contents?

Simple thought or practical experiment:

If he's right then the heating time to bring water to boiling point is independent of the quantity of water. One cup will take as long as two.

If you're right two cups of water will take twice as long to boil.

Is a microwave oven's output power proportional to the mass of its contents? No. The magnetron develops a certain electromagnetic field strength (volts per millimeter or however it is measured) just like any radio transmitter. I tried the experiment, measuring power draw for 2 cups water, 4 and 8, it was identical: 1380 Watts for a 700 Watt rated unit. This is about what we would expect taking in to account losses (most radio transmitters are about 50% efficient).

When operating a transmitter, there is a specification called standing wave ratio, which determines how well matched the source is to the load. If the load is perfectly matched, it absorbs the entire output, regardless of how much power that might be. If it is poorly matched, some of the power is "reflected back" and makes an in-phase voltage at the output terminal of the device.

If this reflected power causes the maximum safe voltage of the output device to be exceeded, it will arc over. It is also possible for a mismatched load to draw too much current, so the device will self-destruct by overheating.

In essence, you have X amount of watts coming out, which will either be properly absorbed by a load, or will stress the device (magnetron in this case) and probably damage or destroy it. The output power is unchanged, and the input draw is unchanged. It is like connecting an electric motor to a load: Stall the motor and it might burn out, unload it and it might overspeed and damage itself.

This is true for all forms of radio wave emission.

Addition: All devices have loss as well, so even if "spinning the wheels" it will still draw and waste some energy. In the case of a Class A audio amplifier, this is 50% of the input power. In some systems it is more, in others less. Since a magnetron is not ideal, it is simply going to draw some power no matter what.

So I have finally gotten around to testing this.

Using this watt meter I tested 0, 1, 2 and 4 cups of water in a plastic bowl.

Overall, there was a difference of roughly 1 watt between any of the quantities of water, including empty.