Blackbody Dynamics 2: Microwave Oven

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Doug Cotton has suggested to use a microwave oven to illustrate aspects of radiative heating connecting to my new derivation of Planck’s radiation law based on a wave model subject to finite precision computation, as discussed in the previous post Blackbody Dynamics.

As we all know a plastic bowl will not get (quickly) heated in a microwave oven from high amplitude/low frequency forcing, while it will get heated by low amplitude/high frequency forcing from the Sun. The question is why?

The finite precision wave model offers the following answer based on different dynamics of internal heating with the forcing frequency below and above the cut-off frequency of the bowl:

1. With the low frequency forcing of the microwave oven below the cut-off frequency of the bowl, but with an amplitude larger than the current blackbody radiation from the bowl,  the bowl will only slowly get heated internally towards radiative equilibrium with the blackbody radiation balancing the forcing.
2. The high frequency forcing from the Sun above the cut-off frequency of the bowl will cause quick heating of the bowl towards equilibrium through the finite precision dissipative mechanism.

We have seen that the dynamics is in principle described by:

• $\frac{dE}{dt} + R + H = F$

where $E$  is the internal energy $R$ outgoing radiation, and $H$ the dissipative mechanism causing heating above cut-off. Case 1. is dominated by the equation $\frac{dE}{dt} = F$ and 2. by the equation $H = F$ with possibly different dynamics as suggested.