What’s the temperature inside a microwave oven?
I’ve seen some thermodynamics textbooks start off with a preliminary definition of temperature that amounts to “The temperature is what a thermometer says it is”, since temperature is really a concept that fundamentally is derived from energy and entropy. So the books like to discuss those at length before talking about the real definition of temperature despite the fact that temperature is what people are accustomed to seeing.
So let’s put a thermometer in the microwave. If it’s a mercury thermometer it will probably rocket up to off-scale high before breaking. An electronic thermometer will simply die instantly. Strictly from the thermometer definition, either a microwave is tremendously hot or hasn’t got a temperature at all. That’s answer number one, and it’s not a very good one. But if you could insulate the thermometer from the radiation and let it reach equilibrium with the air in the oven, it would be pretty much at room temperature. We know this because if you let a microwave run for a little while and then open it up, the air inside isn’t hot. And since air can’t exactly cool instantly, it can’t have been hot while the oven was running.
That’s answer number two. If you define temperature as the average kinetic energy of the air molecules in the microwave, it’s at or near room temperature. This is why it’s very difficult to bake things in a microwave. They’ll get hot, but they don’t brown from external hot air as in a conventional oven. And since “average kinetic energy of the molecules” is the actual physics definition of temperature, this is the answer.
But food placed in an operating microwave will get hot quickly, and that doesn’t happen to objects just sitting in room temperature air. The resolution to this is the fact that food in a microwave oven isn’t getting its heat by conducting heat from the kinetic energy of the molecules in its environment. Instead, it absorbs energy directly from the microwave radiation. Air doesn’t, or at least not particularly well. Thus the temperature of the oven environment is largely immaterial to the cooking process.
Now if you want to you can extend this a little bit, as writers occasionally do in answering questions about the temperature of space. You’ll often hear about the 2.7K cosmic background radiation. This is talking about the microwave radiation that saturates the whole universe, and they say it has a temperature of 2.7 Kelvin because a blackbody heated up to 2.7 Kelvin would radiate the same wavelengths. All other effects aside, a blackbody left floating in space far from any other light source or hot objects will reach that same temperature because that’s the temperature at which it’s radiating energy away at the same pace it’s absorbing energy from the microwave background.
In space near the earth there’s this huge star not terribly far away, and so the energy emitted by the sun will make a blackbody considerably hotter. As a rough estimate, you can use the Stefan-Boltzmann law, plug in the solar constant, and solve for T. Doing this, I get that the blackbody “temperature” of space near the earth is about 123 degrees Celsius. Which is pretty hot. Things like the Space Shuttle don’t get that hot because they’re not blackbodies: they reflect much of the incoming radiation away.