This is a long one, but it is a no solve.
Youʼre cooking four pancakes, one at a time, using a stove-top timer to judge the time Ät needed to cook each
side (i.e. half) of each circular cake (radius = r).
The timer emits a “ding,” a sound whose pressure variation is described by P = Pmaxcos(ùt ± êx). Your ear
is at a distance from the timer that is equal to exactly 7 wavelengths of the sound, and from that distance, the
loudness of the sound is âdinger.
The timerʼs sound power output is just .01% as much as any one of the stoveʼs burners. Youʼre using one of
those burners—but at just 80% of its maximum power —to heat the pancake griddle. That burnerʼs surface
temperature is T burner . The pancake batter (c pancake and âpancake ) is initially at temperature T i and thickness li. The griddle bottom (of thickness L and conductivity k) ) transmits only 25% of the burnerʼs total power to the pancake. Assume that each pancake is cooked evenly, achieving the same final temperature throughout as the inside bottom of the griddle.
As the pancakes are cooked, you stack them neatly and tightly in a dish in the oven (maintaining them at their
fi nal cooked temperature). When all are done, you pour enough syrup (density = ñsyrup), which is also kept at that final pancake temperature, around the pancakes so that the stack is fl oating freely (oh yeah).
What volume of well-chilled butter (density = ñwellchilledbutter) must you place on top so that the entire stack of cakes (but none of the butter) is submerged? (The pancakes do not, alas, soak up any syrup.)
2 answers