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Whenever I put a meal in the microwave which contains cheese, why does the cheese get hot before the rest of the meal is heated through?

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It is because cheese has a nice combination of water and fat. The water is important since the microwave transfers energy to it by making the water molecules vibrate. On the other hand, oils, in general, have lower specific heat (compared to water). This means that given the same amount of heat, the temperature change is higher for fat than for water. You can see in this table as normally fatty food has greater specific heat. Moreover, oils have higher boiling points so the cheese can reach a temperature above $100\ \mathrm{^\circ C}$.

Edit

Both vegetable and animal oils are made of nonpolar molecules. This means that oils cannot be effectively heated up by dieletric heating (microwave absorption). If we consider the limit case where oil does not absorb microwaves at all, then any combination of water and oil (mixture) outperforms pure oil at the rate of heating up under microwaves. The mixture, in this case, heats up because water is absorbing microwaves and is giving up heat to the oil by thermal conduction. On the other hand to compare the performances of the mixture and pure water we need to take into account the specific heat of both substances. If the specific heat of the mixture is sufficiently smaller than the specific heat of the water, then the former will outperform the latter in heating up under microwaves.

Can we heat up oil in a microwave? Oils' molecule, in general, may have a non-zero dipole moment but it is so small that oil's dielectric loss factor is about a hundredth of the water's one. Recall that the dielectric loss factor roughly expresses the degree to which an externally applied electric field will be converted to heat. It is in general dependent of the frequency of the radiation and for water, it is maximum at $2.45\, \mathrm{GHz}$, the frequency of most microwaves oven. By a simple home experiment, one can easily check that conduction plays a major role. Try to get some containers that respond differently to microwaves, that is, test how the empty containers heat up. Then separate one that does not heat up and one that does heat up. Fill them with the same amount of oil and let them on the microwave oven for the same amount of time. The oil in the microwave interacting container will be much warmer. The explanation is that the oil was mainly heated up by conduction. Note that in a homogeneous mixture of oil and water (like a cheese) this conduction is optimized.

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    So the water allows more efficient heat transfer and the fat allows the temperature to be higher for a given amount of heat? – DanielSank Jan 25 '17 at 18:23
  • @DanielSank Exactly. And there must be good balance between the two. I bet parmesan cheese (little water) and a mascarpone (too much water) don't heat up as easy as a provolone. – Diracology Jan 25 '17 at 18:43
  • Does the fat absorb microwave energy as well? If it is only the water absorbing the energy and then distributing it to the fats, it can't get hotter than 100 ∘C. The water would leave the cheese as steam. – Shane Jan 26 '17 at 07:38
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    @Shane No, fats absorb microwaves quite nicely - less so than water, but they get heated up to a higher temperature thanks to their much lower heat capacity. Keep this in mind when microwaving fatty foods - it's really easy to "burn" the fats while the meal is still cold. Ever tried to microwave chocolate or bacon? – Luaan Jan 26 '17 at 08:27
  • @Diracology sorry I've unaccepted your answer because on reflection I believe, based on experimental observation, that there is also something in cheese which makes it more efficient than other materials at absorbing microwaves. I might hold out to see if anybody can substantiate this. – it's a hire car baby Jan 26 '17 at 09:40
  • This answer's wrong in that it seems to suggest that having fats in the cheese allow it to heat up more than water alone. If we accept the (probably true) premise that the water preferentially absorbs microwaves and offloads some of that heat to the fat, then the fat effectively increases the heat capacity of the system, causing it to warm up more slowly. The more fat, the more homogeneous the heating throughout the microwave should be. Another mistake is in implying that a higher specific heat facilities heating; the reverse is true: higher specific heats warm more slowly. – Nat Jan 26 '17 at 09:46
  • @ChemicalEngineer he says "lower" specific heat makes it heat up more. But the first bit of what you say is right. – it's a hire car baby Jan 26 '17 at 09:57
  • @RobertFrost Ah, right, he's talking about specific heat, which is in per-moles or per-units. Still, the total heat capacity increases when there're more content; it still requires more energy to heat up, and if it doesn't receive a proportional increase to heat generation (i.e. if the fat doesn't absorb microwaves as well as water of the same heat capacity), then it's still detrimental to heating. The total heat capacity goes up; the fact that specific heat capacity, which is an intensive property (as opposed to extensive property), decreases is a red herring. – Nat Jan 26 '17 at 10:01
  • @ChemicalEngineer Of course if you add fat to a portion of water you increase the heat capacity. But if you add fat and remove the same amount of water, then you decrease the heat capacity of the system. Or we can just talk about specific heat as Robert suggested. – Diracology Jan 26 '17 at 11:35
  • @Diracology If you add fat and remove the same amount of water, you also decrease microwave absorption. Keep doing it, you eventually get to pure fat; lower heat capacity, but also lower microwave absorption. – Nat Jan 26 '17 at 11:36
  • @ChemicalEngineer You are absolutely right. That's why I said in the answer there must be a "nice combination" of water and fat. I meant a "optimal combination". – Diracology Jan 26 '17 at 11:38
  • @Diracology Absent a second-order effect, it's just a linear combination. The optimum is then necessarily either pure water or pure fat. – Nat Jan 26 '17 at 11:38
  • @ChemicalEngineer For example, pure fat will heat up slower because microwaves excite water molecules. Pure water on the other hand is not so effective in using heat to increase its temperature (high specific heat). And the most important (in my opinion) is that fat can reaches temperatures higher than 100C, that is why the cheese is always so hot. – Diracology Jan 26 '17 at 11:43
  • @Diracology Consider a hypothetical combination of water and fat, in which the heat capacity and microwave absorption are proportional to whatever concentration of water and fat you have. Heating is then at the microwave absorption rate divided by the heat capacity. Without second-order effects, this is basically a constant for a given mixture composition; and if you vary the composition fraction, then the optimum is necessarily a pure substance (either pure water or fat). – Nat Jan 26 '17 at 11:45
  • @Diracology I think that you're correctly realizing that the decreased specific heat helps, but improperly ignoring the decreased absorption. There's no second-order property to the mechanism that you've described. It can't work. Except, your note about maximum temperature - that holds. You're correct that cheese should be able to get a few degrees hotter than water, at the maximum end of the scale (though it'll also dry out and turn to black char at that point). – Nat Jan 26 '17 at 11:47
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    Both @ChemicalEngineer and Diracology - the ability of the fat to go above the boiling point of water is irrelevant. As long as there is any water in the fat, fat cannot get that hot either. What is relevant is the limited power of the microwave. How much cheese will saturate that factor, to the point of perfect absorption? And how much water? – Jirka Hanika Jan 26 '17 at 17:28
  • Could you add some analytical model for what you think is going on? I mean, you're not wrong about the physical facts; just, the conclusions don't follow from the premise. I feel like this would become apparent if you wrote out the equations. – Nat Feb 01 '17 at 17:01
  • It is bizarre that this is the most upvoted answer given that a simple test of putting pure vegetable oil in a microwave clearly shows that it heats up nearly as well as water. – user1247 May 28 '18 at 15:40
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The solid structure of cheese helps prevent steam loss

Water absorbs microwaves well, primarily at the boundaries since the water at the boundaries absorbs most of the microwaves before they get deeper into the body of water. If you heat water alone, its boundaries get most of the heat; then, steam can escape, causing much of that absorbed heat to be lost. This results in a powerful cooling effect called evaporative cooling.

Evaporative cooling is an important effect in microwaves. For example, if you get a microwavable dinner, it'll often tell you to cut a slit in the overwrap without actually removing the contents. The slit allows steam to escape a bit so that pressure doesn't cause the bag to pop, but it still keeps in more steam to help retain heat. This reduces evaporative cooling.

Cheese's solid structure should have a similar effect. This is, the water isn't free to just escape as steam, so the heat it captures isn't so easily lost.

Not really about fats and water working together

The currently up-voted answer asserts that cheese and fats work together using their differing levels of microwave absorption and heat capacity to warm up faster than either alone.

Unfortunately this can't be true because it's an entirely first-order mechanism. Fats and water would both heat up at some rate proportional to the microwave absorption divided by their heat capacity, i.e. $$\frac{\text{d}T}{\text{d}t}{\propto}{\frac{\left[\text{absorption ability}\right]}{\left[\text{heat capacity}\right]}}$$ If you combined them without a second order effect, then their combined absorption ability and heat capacity are both a weighted average of the pure values for each, i.e. $${\left.\frac{\text{d}T}{\text{d}t}\right|}_{\text{cheese}}{\propto}{\frac{{x}_{\text{water}}{\left[\text{absorption ability}\right]}_{\text{water}}+{\left(1-{x}_{\text{water}}\right)}{\left[\text{absorption ability}\right]}_{\text{fat}}}{{{x}_{\text{water}}\left[\text{heat capacity}\right]}_{\text{water}}+{\left(1-{x}_{\text{water}}\right)}{\left[\text{heat capacity}\right]}_{\text{fat}}}}$$ Then, let's assume that absorption ability and heat capacity are constant for both fat and water (which isn't really true, but a reasonable simplification). Then, regardless of the actual values for the absorption abilities and heat capacities, there is no combination that can outperform both pure substances. If both pure substances heat up exactly as fast, then their combination should do the same. But if one heats faster, then the more of it the combination has, the faster the combination'll heat. That is, if we optimize ${x}_{\text{water}}$, we'll necessarily find either ${x}_{\text{water}}=0$ (pure fat) or ${x}_{\text{water}}=1$ (pure water) as the optimal solution.

When a combination works like this, there must be a higher-order effect at work. In this case, I'd suspect that the most important higher-order effect is that cheese traps the steam, such that the water molecules that happen to trap the most heat don't just fly away.

Not really about boiling points

Some have pointed out that water boils at ${100}^{\circ}\text{C}$, so the fats might assist by being able to be hotter. As @JirkaHanika pointed out, this isn't really relevant because water isn't bothered by this until it actually hits its boiling point of ${100}^{\circ}\text{C}$.

If you're microwaving your pizza to be that hot, then you're drying it out. This YouTube video shows a guy putting a cup of water in the microwave with his pizza to help keep the crust crispy:

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  • I agree cheese has less capacity to cool itself through latent heat loss (than does water); this is definitely a component of it. – it's a hire car baby Jan 26 '17 at 09:57
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    @RobertFrost Energy's conserved, so heating can only be done by microwave absorption or exothermic reaction. Fats do store a lot of energy that can drive exothermic reactions, as that's their primary biological function (they're basically batteries). Still, unless they're somehow undergoing chemical change, it's going to be a simple matter of the heat from the microwaves accumulating - and then being partially lost through cooling, e.g. evaporative cooling. The primary source of variation's going to be how effective the cooling mechanisms are; anything else violates conservation of energy. – Nat Jan 26 '17 at 10:21
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    @RobertFrost Well, mostly. Technically, there's an enthalpy of mixing that'll change with the composition as the cheese deforms due to microwaves heating it up. But, per Le Chatelier's principle, that change in enthalpy of mixing will be a resistive force, not a heating force. – Nat Jan 26 '17 at 10:25
  • @RobertFrost Some say the cheese will melt with fat, some say with steam / From what I've tasted of Kraft meals / I hold with those who favour steam. / But if I had to reheat twice, / I think I know enough of cheese / To say that for burning my mouth fats / Are also great / And would suffice. – lowercasename Jan 26 '17 at 11:00
  • Suppose fat doesn't absorb microwaves at all. Then any combination of water and fat would outperform fat! The formula you wrote for the heating rate of the combination is not right because it neglects the fact that water and fat are exchanging heat by thermal conduction. That is the whole point of the combination. – Diracology Jan 31 '17 at 19:19
  • @Diracology As explained above, one of the pure states will be optimal; in your example, it'd be pure water, i.e. $x_{\text{water}}=1$. As for "neglecting" thermal conduction, exactly what effect do you think it has? How would you model the equations? – Nat Feb 01 '17 at 03:25
  • The point is that you are considering that fat only heat up by microwaves. If that was true, your equation and your claim was right. But there is conduction from water to fat and that is the relevant fact. – Diracology Feb 01 '17 at 12:29
  • @Diracology No, both fat and water are heated by the microwaves, and that captured energy must be used to raise their temperature given their combined heat capacity (either a sum if you're using extensive properties or the weighted average if you're using intensive properties). Don't you remember ideal solutions from Intro to Classical Thermo? My above model assumes ideality, and as noted to my comment RobertFrost, deviations from ideality will tend to be resistive due to Le Chatelier's principle. What non-standard assumptions are you making? – Nat Feb 01 '17 at 12:42
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    Oils and fats are formed by nonpolar molecules. Fact! Microwaves heat up food by vibrating polar molecules. So, fats absorb much less microwaves than water. – Diracology Feb 01 '17 at 12:50
  • @Diracology Correct. The fat and water both collect heat at differing rates (${\left[\text{absorptive ability}\right]}{\text{fat}}$ vs. ${\left[\text{absorptive ability}\right]}{\text{water}}$), and they share that combined heat capture to raise their combined temperature given their combined heat capacity, as in the above equation. What's the part that you're doing differently? – Nat Feb 01 '17 at 13:00
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I think that the key point in the first answer is oils have higher boiling points so the cheese can reach a temperature above 100 ∘C.

If you heat water, when it reaches 100C it will start boiling and all microwave energy deposited thereafter will be converting water to steam, which promptly escapes.

In cheese, water is emulsified with fat. (I don't know if it's small droplets of water encased in fat or vice versa. I'd guess the former since it's more than 50% fat). In any case, I think it will be possible for the water to become somewhat superheated without turning to steam in this environment, where it's got a very large amount of water surface in contact with fats which can be heated above 100C without boiling. In other words, the mixture with fat may suppress steam-bubble formation and growth.

Also the water in cheese is derived from milk, which means it will contain a very significant amount of water-soluble milk proteins. These long-chain molecules may also serve to stabilize the water at >100C (especially if they have hydrophilic parts and hydrophobic parts, which will tend to bind between the water and fat where the two touch). They may even allow pressure in the water droplets to somewhat exceed ambient atmospheric pressure.

The obvious experiment is to measure the temperature of cheese freshly heated in a microwave, or even during heating. For the former melt it in a well-insulating container (I'd suggest a smallish cheese sample in a hole in an expanded polystyrene block, and a large mug of water in the oven at the same time so most of the microwave energy has somewhere else to go). For the latter you'll need a completely non-metallic thermometer which does not significantly absorb microwaves and which reads well above 100C, which might be an interesting bit of research in itself. My guess is that the cheese will reach a few degrees above 100C.

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