A sphere initially at 0∘ has its surface kept at 100∘ from t=0 on (for example, a frozen potato in boiling water!). Find the time-dependent temperature distribution. Hint: Subtract 100∘ from all temperatures and solve the problem; then add the 100∘ to the answer. Can you justify this procedure? Show that the Legendre function required for this problem is P0 and the r solution is (1/r)J1/2 or j0 [see (17.4) in Chapter 12]. Since spherical Bessel functions can be expressed in terms of elementary functions, the series in this problem can be thought of as either a Bessel series or a Fourier series. Show that the results are identical.