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My anecdotal observations (which could be incorrect, they're totally unscientific) indicate that it takes almost as long to evenly heat a big bowl of soup in a microwave as it does to heat it on the stove - 4-5 minutes in my most recent example. Yet a plate of meat or vegetables is reheated in 30 seconds or less.

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What kind of soup? –  Nick Josevski Nov 10 '10 at 23:00
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What makes your microwave "better" than a stove at heating things is that is rather efficient at getting the heat into your food - the wave field permeates the food and resonates with dielectric molecules, which then distribute their rotational energy to their surroundings as heat. This does not rely greatly on heat conductivity inside the food since it is heated locally.

On a stove, all the heat comes from the burner below and somehow has to get to your food - first by transfer from the hot gas/plate to the vessel, and then from that vessel to food. This process is highly inefficient for food that is not in good thermal contact with the vessel - you get a very hot pot and warm air in the room. For water or your soup on the other hand, the thermal contact with the vessel is excellent and almost all the heat that is transferred to the vessel actually ends up in your food.

In the end, the fact that the times for microwave and stovetop heating come out close is mainly an artifact of the fact that your stove outputs much more power than the microwave - a 9000 BTU/hr burner is equivalent to about 2.6 kW, while your usual microwave outputs less than half of that) , but is a lot less efficient. For non-liquid foods, the stove is even less efficient while the efficiency of the microwave doesn't change much.

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This is right, though the essential difference here between the water and the solid food is that in water, the fluid is free to flow, so heat can freely move in convection currents from the bottom of the plate to the top. In solid food, the molecules are held in fixed locations, and conduction is the only available route of heating, and conduction is much slower than convection. –  Jerry Schirmer Jan 25 '11 at 3:07
    
Two errors: There is no "rotation" of molecules in liquid water. Heating by microwaves results from relaxation of orientational polarisation. Microwaves have efficencies of about 60 to 70 % only. –  Georg Jan 25 '11 at 3:51
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That's because water has a higher heat capacity (the amount of energy it takes per kilogram to increase the temperature by 1 degree) than meat or vegetables and since a bowl of soup typically weighs more than a carrot or a piece of chicken, more mass needs to be heated, which takes more energy and thus more time. While meat and veggies do cotain a significant amount of water, a bowl of soup is essentially all water.

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Veggies are basically all water, too. This answer doesn't address the question, which is about the difference between stove and microwave heating. The heat capacity is the same regardless of whether you're heating on the stove or in the microwave. –  Mark Eichenlaub Nov 11 '10 at 5:25
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Downvoted because it misses the point that Thomas Themel's answer notes which is the most important issue here. The speed of heating is related to the power input and the ability to convert that power into heat in the food. Stoves are more efficient for liquids than they are for other types of foods. –  inflector Jan 8 '11 at 19:55
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The wavelength of the microwaves inside your microwave oven is somewhere around 3 cm, or a little more than an inch. When the oven is on, the microwaves inside its cavity tend to form standing waves. This means that there are nodes in the electromagnetic waves every 1.5 cm or so, which are places within the oven at which the amplitude of the waves is always zero. Since the energy of the wave at a given point is proportional to the square of its amplitude, these nodes correspond to points at which the oven is not delivering any energy to the food.

As a side note, the existence of the nodes allows for a neat experiment that can be performed to measure the speed of light using marshmallows in a microwave. See, for example, this website. Briefly, the bottom of a microwave oven (without a spinning platter) is covered in marshmallows and the oven is turned on. Some marshmallows start to melt, while others are unaffected -- corresponding to the locations of the nodes. Measuring the distance between them can tell you the wavelength of the radiation which, combined with the stated frequency of the oven, lets you calculate an experimental value for the speed of light!

The existence of these nodes is the reason that most microwave ovens have a rotating platter: the food gets moved through the nodes, but also through the regions that deliver heating energy to it, and on average all of the food is supposed to heat. In practice though it does often seem, at least anecdotally, that some parts of the food just receive a higher dose of energy than others. This can lead to soup that is hot in some spots, and still cold in others -- a problem that can be somewhat alleviated by stirring the soup periodically, encouraging the soup to reach thermodynamic equilibrium more quickly.

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Indeed, the experiments to measure the speed of light were discussed in this question physics.stackexchange.com/questions/357/… –  j.c. Nov 11 '10 at 23:31
    
This is right, exept the wavelength is about 12 cm –  Georg Jan 25 '11 at 3:50
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The design frequency for microwave ovens is 2450 MHz.

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+1, upgraded again to protect the habit to tell truth :=) –  Georg Jan 25 '11 at 13:42
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