Radiation absorption and resultant temperature rise I have a doubt about radiation absorption and temperature increase. I was taught that the larger heat capacity of diatomic molecules over monoatomic molecules is the result of the possibility that the diatomic molecules may absorb some photon and begin vibrating or rotating instead of getting an increase in translational speed (which is proportional to the measured temperature).  So, some of the energy that impinges on a molecule goes into vibration instead of raising the temperature, but in a monoatomic molecule the only interaction can be the increase of translational speed because there are no vibrational or rotational modes.
But now I learned that water molecules absorb the microwaves in an oven into the vibrational mode and this is what increases the temperature.  See Charles H Martin's comment here.
Can anyone explain the apparent contradiction? If absorbing in the vibrational mode does increase temperature, then what is the proper explanation for the higher heat capacity of diatomic molecules over monoatomic molecules?
Thanks
 A: Mathematically it’s easy to see. Specific heat is defined as the temperature derivative of internal energy. And since there’s translational, vibrational and rotational energy contributing in polyatomic molecules, the specific heat is scaled similarly. See here for details. 
Intuitively speaking, consider a box filled with polyatomic gas. Let us try to measure the temperature of the gas by sticking in a thermometer. The temperature of the gas can only be measured when there are gas particles colliding with the thermometer to transfer the energy. But if part of the energy is stored as vibrational and rotational, these don’t contribute much to the energy transfer. It is in this sense we say that polyatomic gases can store more heat without contributing to temperature which implies higher specific heat. 

Now coming to your question, when we microwave water, it absorbs the photons and this is converted to the rotational (not vibrational, that’s IR) energy if the water molecules. This by definition is increasing the energy of the system, it is heating the system. And that’s why the temperature rises. Now because polyatomic systems have higher specific heat this just means that we need to heat more to increase the temperature by a unit as compared to a monoatomic gas. 
In other words, if you took two systems (one mono and one poly) that absorb a given microwave wavelength at a temperature $T$ and microwave them for a fixed amount of time, the monoatomic gas would have a higher final temperature than the polyatomic gas. Because the polyatomic has more ways to store the energy. This is the effect of specific heat. 
