Heating effects of microwaves I understand the heating effect(dielectric heating) of microwaves. This heating is caused by using  a frequency of  2.45 GHz and this is the same frequency at which Bluetooth works and the L and S bands of communication.   
The intensity of microwaves used for communication is very less than used in microwave oven. 
What is the numerical value of microwave heating as a function of intensity (for example, in the case of a mobile phone and a microwave oven). And how can I calculate it?
Note: I have gone throught this post Could cell-phone radiation cause cancer?  and the related wikipedea article http://en.wikipedia.org/wiki/Mobile_phone_radiation_and_health. I know there are not any adverse effects of microwaves but I want to be sure that's why I want to know the numerical figures.
 A: A microwave oven :

A microwave oven converts only part of its electrical input into microwave energy. An average consumer microwave oven consumes 1100 Watts of electricity in producing 700 W of microwave power, an efficiency of 64%

So within the cavity it is something like 700Watts
Blue tooth :

The Bluetooth specification targets power consumption of the device from a "hold" mode consuming 30 micro amps to the active transmitting range of 8-30 milliamps (or less than 1/10th of a watt). 

100milliwatts top, from the link.
These numbers tell me
a) that the energy needed to cook a kilo of meat in 10 minutes or boil water in a cup in 1 minute is about 7000 times higher than the highest energy consumed by Bluetooth.
b)The microwave is a cavity resonator trapping the energy. Blue tooth is an antenna, radiating and necessarily following the 1/r^2 fall of intensity of radiated electromagnetic energy. At a distance from the ear(1cm) of even 20cm the impinging energy energy will fall 400 times. That is why people who are fastidious or overly scared, or who are always on their mobile use the "hands free" supplied with the instrument.
A: Light of any wavelength can cause heating. It depends on the material which absorbs it. Few materials absorb light present in microwave range while others simply reflect them . Consider a material which absorbs light at microwave frequencies. If the intensity of the light wave at microwave frequencies is increased then heating effect will also be observed. This phenomenon is due to light waves exciting electrons in the medium which absorbs it.
Black body radiation is the phenomenon dealing with absorption and re-radiating the absorbed light. where ε is At any given wavelength λ, emissivity is defined as the ratio of the actual emitted radiance, Rλ, to that from an ideal blackbody, Bλ
ελ = Rλ / Bλ .
Emissivity is a measure of how strongly a body radiates at a given wavelength; it ranges between zero and one for all real substances. A gray body is defined as a substance whose emissivity is independent of wavelength. In the atmosphere, clouds and gases have emissivities that vary rapidly with wavelength. The ocean surface has near unit emissivity in the visible regions.
For a body in local thermodynamic equilibrium the amount of thermal energy emitted must be equal to the energy absorbed; otherwise the body would heat up or cool down in time, contrary to the assumption of equilibrium. In an absorbing and emitting medium in which Iλ(intensity in layman terms) is the incident spectral radiance, the emitted spectral radiance Rλ is given by
Rλ = ελBλ = aλIλ ,
where aλ represents the absorptance at a given wavelength. If the source of radiation is in thermal equilibrium with the absorbing medium, then
Iλ = Bλ , so that ελ = aλ .
This is often referred to as Kirchhoff's Law. In qualitative terms, it states that materials that are strong absorbents at a given wavelength are also strong emitters at that wavelength; similarly weak absorbents are weak emitters.
Coming to microwave heating of human bodies one needs to keep in mind that free radicals cause cancer. Microwave heating increases the number of ions. Your project must find a link between microwave heating and concentration of free radicals. Though microwave frequencies donot have enough energy per quanta to ionize molecules it is still worth a try.
Edit 1- @Floris Yes you are right. I have changed it. Free ions cause cancer, antioxidants reduce them. Never mind I hope this explanation might be useful. But microwave waves just heats the body fluids. The heat may increase number of free ions but not the microwave radiation. Gamma rays and x-rays are powerful enough to create free ions. Maybe the heating might cause some effects but there is no support that microwaves cause cancer. 
