In Fahrenheit 451, Ray Bradbury writes about firemen whose job it is to burn books. The 451 refers to the temperature \(\left(232.8^{\circ} \mathrm{C}\right)\) at which paper starts to burn. Assume we have a \(4 \mathrm{~cm}\) thick book thrown atop a fire burning from below. The fire provides a temperature of \(650^{\circ} \mathrm{C}\) and the pile limits the heat-transfer coefficient to the book to be \(450 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\).

The properties of paper are:

\[C_{p}=850 \frac{\mathrm{J}}{\mathrm{kgK}} \quad k=0.7 \frac{\mathrm{W}}{\mathrm{mK}} \quad ho=950 \frac{\mathrm{kg}}{\mathrm{m}^{3}}\]

a. Assuming the book starts out at \(25^{\circ} \mathrm{C}\), how long will it take the surface of the book in contact with the pile to ignite?

b. Based on your answer to part (a), what is the temperature on the side of the book exposed to the atmosphere? Is the semi-infinite approximation valid?