Question

Penguin huddling. To withstand the harsh weather of the Antarctic, emperor penguins huddle in groups. Assume that a penguin is a circular cylinder with a top surface area $$a=0.34\ m^{2}$$ and height $$h=1.1\ m$$. Let $$P_{r}$$ be the rate at which an individual penguin radiates energy to the environment (through) the top and the sides); thus $$NP$$ is the rate at which $$N$$ identical well separated penguins radiates. If the penguins huddle closely to form a huddled cylinder with top surface area $$Na$$ and height $$h$$, the cylinder radiates at the rate $$P_{h}$$. If $$N=1000$$
what is the value of the fraction $$P_{h}/NP_{r}$$

Answer 1