Volume of a speaker needed to boil an egg
I have a fun question to ask that me and my friends couldn't figure out. If I was to boil an egg using a speaker, how loud would that speaker need to be? (Yep, this is clearly what keeps us physicists entertained!) Let's assume the speaker is a distance $d$, $1m$ away from the egg. I imagine it is quicker to boil the egg not in water, so let's say the egg is placed in front of the speaker. The only thing in the room is the egg and speaker. My extremely approximate solution is as follows: Let the mass of the egg $m$ be $45g$. The heat capacity $C$ of an egg shell is 888 $J/K kg$, whereas the white and yolk are more towards $3500 J/K kg$. 842
I will assume that the egg has a constant heat capacity of $3000 J/K kg$. What equations can we use? We know that the energy, $Q$ from heating an object by a temperature change$ \Delta T$ is , $$Q = m C \Delta T $$ Power $P$ can be expressed as $\frac{Q}{t} = I 4\pi d^2$, where $I$ is the intensity of the sound. The intensity of the sound in Decibels, $\beta$, is given as follows, $$ \beta = 10\log_{10} (\frac{I}{I_0}),$$ where $I_0$ is given as $10^{-12} W/m^2 $. Plugging all the above in leaves us with, $$\beta = 10\log_{10} (\frac{mC \Delta T}{4\pi d^2I_0t})$$ I like my eggs quite runny, so I will say that $t = 5min$. Let's aim to get the temperature of the egg up to $80$ degrees celsius from $20$ degrees celsius. Inputting all these numbers gives me $\beta = 123.32 W/m^2 $, approaching that of the volume of a jet engine.
I have made huge assumptions throughout this, and was wondering if anyone had any better ideas on how to accurately calculate the volume needed? For instance, modelling the egg as having one heat capacity is erroneous, and I have not considered sound absorption in the room. 842