Heating cup in microwave?

I heated my milk cup in the microwave today and noticed that the cup was hot but not the handle. Even if I heat it too much , cups handle temperature remains the same. How is that possible?

• what is your milk cup made of? – Bob D Oct 18 '20 at 20:49
• It is made of glass – user277437 Oct 19 '20 at 3:34
• It would be nice if you could measure (and report) the temperature of the cup in different heating scenarios. – Superfast Jellyfish Oct 19 '20 at 5:22

It's probably because your milk cup is made of a material that is a relatively good thermal insulator.

First of all, the microwaves directly heat the milk, and not the cup, as long as the cup is made of material that microwaves pass through without being absorbed.

The heated milk, in turn, being in contact with the sides of the milk cup directly heats the sides but does not directly heat the handle because the milk is not in direct contact with the grasped portion of the handle. For the handle to get warm there needs to be heat transfer by conduction from the sides of the cup to the handle.

The heat transfer from the sides of the cup to the grasped portion of the handle will depend on the thermal conductivity of the cup material, the cross sectional area of the handle part of the cup, and the length of the path from the side of the coffee cup to the part of the handle being grasped. If your milk cup is made of glass, it's thermal conductivity is relatively low (roughly 1 W/m K) making it a reasonable thermal insulator.

All of the above factors can keep the grasped portion of the handle from getting too hot regardless of how hot the milk is, at least for a reasonable amount of time.

Hope this helps.

• "1 W/m⁰K" looks like a mangled unit to me. The superscript zero would cancel out the metre unit. If it was supposed to mean degree, then kelvins must not be written with degree. I think you meant to write "1 W/(m·K)"? – Nayuki Oct 19 '20 at 6:06
• superscript means degrees Kelvin – Bob D Oct 19 '20 at 6:52
• @BobD there has been no "degrees Kelvin" since 1967. The unit is absolute. robertpatrick, the molecules of liquid absorb the energy of the microwave and increase their own energy as a result (i.e. they heat up) this is easy for them as they move freely around in the liquid. The solid mug cannot absorb the microwaves as the molecules in the cup can't move around and get excited by the wave. – rbrtl Oct 19 '20 at 10:10
• @TonyK The middle dot means multiplication. The SI unit for thermal conductivity is "W / (m · K)". If you write it as "W/m K", it is unclear if that means "(W/m)×K" or "W/(m×K)". Actually the important part is the parentheses, not the dot. It is also correct to write "W/(m K)", but the space might get dropped accidentally, but "mK" is millikelvins which is wrong. – Nayuki Oct 19 '20 at 15:24
• You can verify Bob's answer (i.e., that the container does not absorb microwaves) by microwaving the milk cup (empty) and a microwave-safe cup of water in your microwave. If the milk cup is microwave safe, neither the cup nor the handle will heat up. Note: Don't skip the cup of water. If your microwave is turned on and has nothing to microwave, it will microwave itself instead. This will damage your microwave. – Brian Oct 19 '20 at 17:17

Like Bob has mentioned, the container doesn’t absorb the microwave. The reason for this lies in quantum mechanics according to which the energy levels of atoms are quantised. This means the atom can’t have any arbitrary energy and can only absorb energy corresponding to the difference of the allowed energy levels (see figure below).

Microwave ovens radiate light having discrete energy chunks of $$10^{-5}$$ eV. This frequency is particularly chosen because water has energy level separation such that it strongly absorbs this light. And since most food we consume contains water, this is an efficient way of heating them provided that the container doesn’t absorb/reflect any of it. Glass and ceramics don’t have energy level separation corresponding to this frequency so they don’t absorb any.

So the only process by which it is getting heated up is by conduction through the water it is containing.

Even if I heat it too much , cups handle temperature remains the same.

Strictly speaking, this isn’t true. There will be some temperature difference in the two cases where you heat the water to different extents. However, depending on the material properties (thermal conductivity, shape) and the timescale at which the container is picked up, the temperature difference in the two scenarios might not be resolved by our hand as they are terrible at quantifying temperature.

So I recommend you to measure the temperature for different heating conditions and see if the temperature difference is resolvable by say an IR thermometer.

• Can the downvoter share their reason(s) to do so? Feedback would be helpful. – Superfast Jellyfish Oct 20 '20 at 7:41