# Why does the left cup’s top region till where the water is filled the most hot point and not the points below?

So I have two cups here. Black cup on the left and a white cup on the right.The region where I have made a dark red horizontal line is the region till where the water is filled.The left one is made of plastic and the right one is made of ceramic.

Now, when I heated both the cups in my microwave .Only the top region or till where the water filled for the left cup , it was the hottest region from the top and as I slowly touch it and go downwards. That is the reason I have also drawn a ↓ symbol for the left cup.

Now , for the right. All the regions are equally hot.

What I noticed was that the left had a decreasing radius as we go down below or it looks like a cone if we place it upside down. For the right cup , it is not the same case. This is just my assumption.

What is the real reason that this is happening ?

Also , if you heat both the cups for 1min separately in microwave .

The top region of black cup is more hotter than any region on the white cup.Why does that happen ?

Do let me know if you have any difficulty in understanding my question .

• Are they of the same materials?
– lee
Jan 14, 2021 at 8:50
• The left one is plastic and the right one is ceramic.@lee Jan 14, 2021 at 9:12
• Just to be sure, the hottest part of the right cup is above the water? Have you tried with a cup half-full or less (microwave for appropriately shorter time)? Jan 14, 2021 at 10:51
• No. I am talking about left cup. The hottest part is till where I filled the water with dark red line.Also, yes I tried with hale and more less than half also.Same results @Toffomat Jan 14, 2021 at 13:55
• Interesting question. Jan 17, 2021 at 11:05

Microwave ovens heat up food and drinks by oscillating water molecules in the food/drink thereby increasing the temperature of these molecules, and therefore the temperature of the food/drink.

The laws of thermodynamics tell us that the higher the temperature of a material, the more thermal energy it has. And at a given temperature, the more of a particular substance, the more total thermal energy this substance will possess when it gets heated up.

In fact, the heat capacity (ability to absorb heat) is given by

$$\Delta Q = C m \Delta T$$

where $$Q$$ is the amount of heat that must be added to the water of mass $$m$$ in order to raise its temperature by $$\Delta T$$, and $$C$$ is called the specific heat capacity which is a constant for different substances. Note how the greater the mass, the greater the thermal energy that will be present.

The heat capacity for water is relatively high than compared with solids. On a molecular level, the microwaves cause the atoms of a solid to vibrate toward and away from each other like they were connected by a spring. As the temperature is increased, the frequency/energy of these vibrations increases. In a solid, this is basically the only motion available. In a liquid like water (and gases), absorbed heat energy causes the atoms in the $$H_2 O$$ molecule to vibrate and rotate as well as translate. This means there are more possible microstates for the water molecules and because of this their heat capacities are larger than in solids. So if what we place in the microwave an object with more water content, the hotter the object will get compared to one with smaller water content (all other parameters being equal like size of objects, microwave power, initial temperatures of objects, cooking time etc).

Possibility one:

If we look at the left cup, we see that it is conical in shape (consider the volume per say each millimetre of height) and so there will be a greater volume of water at the top than at the bottom. This means there will be a greater mass of water absorbing energy by the microwaves at the top of the cup than at the bottom, resulting in a thermal energy gradient with a higher temperature at the top and a lower temperature at the bottom. And since the cup’s volume decreases uniformly as we move down to the bottom of the cup, so to will the temperature of the water.

We would not expect the same for the cup on the right. In fact we would expect that on average, the temperature would be the same at the top of the cup as we move down to the bottom - we also assume the the microwave transmits its radiation uniformly throughout the microwave compartment.

This seems consistent with your experimentally determined results.

Possibility two:

Microwaves also have a particular pattern of standing waves in the compartment. This could go to explaining why the conical cup had hotter water at the top than the bottom. But why would the ceramic cup have a consistent water temperature from top to bottom? A possible explanation is that microwaves are not interacting directly with the water, but with the mug itself. So the microwaves are heating the upper part of the cups directly, and even if the standing waves form at the "top regions" of the cups, there may be conduction down the length of the cup. If the cup heats up this way, then as it transfers this heat to the water, the temperature at the top would be the same as the bottom.

• Ok.Thank you.One more thing that temp is very less as compared to the top in the left cup? Jan 14, 2021 at 9:42
• I really couldn’t say without doing the experiment myself, but would guess that the temperature difference between a top and bottom would be “noticeable different” but not terribly different. Can you do the same experiment with a thermometer, or even better, a thermal camera? Jan 14, 2021 at 9:50
• I’ll try thermometer and update the readings. Jan 14, 2021 at 10:14
• Ok. Excellent.. Jan 14, 2021 at 10:20
• Be careful with the thermometer so that it does not pick up the temperature of the water at the top as you plunge it down into the cup. You may be able to get around this by placing the thermometer in the cup with the water before you put it in the microwave. But this is still messy. Can you get hold of a thermal camera - borrow one? Jan 14, 2021 at 10:27